SATYAM TIWARI

[satyamti1250]

Week 1 ICNSA using all the data

library(reprex)
library(fredr)
library(ggplot2)
library(forecast)
#> Registered S3 method overwritten by 'quantmod':
#>   method            from
#>   as.zoo.data.frame zoo

#set api key for fredr
fredr_set_key("619954596c335c6cd3c4fc1f7a346118")

#read the ICSNA data 
time_series_data <- fredr(series_id = "ICNSA") 

time_series_data$date <- as.Date(time_series_data$date)

#plot of claims 
ggplot(time_series_data, aes(x = date, y = value)) +
  geom_line() +
  labs(title = "Claims Data",
       x = "Year",
       y = "Number")

acf(time_series_data$value)

pacf(time_series_data$value)

ts_data <- ts(time_series_data$value, frequency = 52)

arima_model <- arima(ts_data, order = c(1,0,0))

forecast_week <- predict(arima_model, n.ahead = 1)
print(forecast_week$pred)
#> Time Series:
#> Start = c(58, 16) 
#> End = c(58, 16) 
#> Frequency = 52 
#> [1] 242433.4

Reason for selecting Model:

ACF plot shows a quick decay and PACF plot has a notable spike at lag 1, with all other lags being pretty much inside the confidence interval. The strong correlation at lag 1 suggests that the current value of the series is significantly correlated with its immediate past value. Hence,the AR(1) model is supported.

^{Created on 2024-02-08 with reprex v2.1.0}

[satyamti1250]

Week 2 Filtering out the data during covid

library(dplyr)
#> 
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#> 
#>     filter, lag
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, setequal, union
library(fredr)
library(ggplot2)
library(forecast)
#> Registered S3 method overwritten by 'quantmod':
#>   method            from
#>   as.zoo.data.frame zoo

#set api key for fredr
fredr_set_key("619954596c335c6cd3c4fc1f7a346118")

#read the ICSNA data 
time_series_data <- fredr(series_id = "ICNSA") 

covid_start <- as.Date("2020-02-14")
covid_end <- as.Date("2021-01-02") 

time_series_data$date <- as.Date(time_series_data$date)
#Remove the covid dates 

time_series_data_filtered <- time_series_data |>
  filter(!(date >= covid_start & date <= covid_end))

#plot of claims 
ggplot(time_series_data_filtered, aes(x = date, y = value)) +
  geom_line() +
  labs(title = "Claims Data",
       x = "Year",
       y = "Number")

acf(time_series_data_filtered$value)

#Auto Correlation Plot 

pacf(time_series_data_filtered$value)

#Auto Correlation Plot 

ts_data <- ts(time_series_data_filtered$value, frequency = 52)

arima_model <- auto.arima(ts_data)

forecast_week <- predict(arima_model, n.ahead = 1)
print(forecast_week$pred)
#> Time Series:
#> Start = c(57, 21) 
#> End = c(57, 21) 
#> Frequency = 52 
#> [1] 237781.5
#Printing the values removing covid data

Unsure of the model selection hence going with auto arima ^{Created on 2024-02-08 with reprex v2.1.0}

[satyamti1250]

HW1 from UB learns

library(dplyr)
#> 
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#> 
#>     filter, lag
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, setequal, union
library(fredr)
library(ggplot2)
library(forecast)
#> Registered S3 method overwritten by 'quantmod':
#>   method            from
#>   as.zoo.data.frame zoo

fredr_set_key("619954596c335c6cd3c4fc1f7a346118")

icnsa <- fredr(series_id = "ICNSA") 

icnsa$date <- as.Date(icnsa$date)

unemployment_rate <- fredr(series_id = "UNRATE")

unemployment_rate$date <- as.Date(unemployment_rate$date)

summary(icnsa)
#>       date             series_id             value         realtime_start      
#>  Min.   :1967-01-07   Length:2980        Min.   : 133000   Min.   :2024-02-21  
#>  1st Qu.:1981-04-16   Class :character   1st Qu.: 265800   1st Qu.:2024-02-21  
#>  Median :1995-07-25   Mode  :character   Median : 326919   Median :2024-02-21  
#>  Mean   :1995-07-25                      Mean   : 365013   Mean   :2024-02-21  
#>  3rd Qu.:2009-11-01                      3rd Qu.: 406725   3rd Qu.:2024-02-21  
#>  Max.   :2024-02-10                      Max.   :6161268   Max.   :2024-02-21  
#>   realtime_end       
#>  Min.   :2024-02-21  
#>  1st Qu.:2024-02-21  
#>  Median :2024-02-21  
#>  Mean   :2024-02-21  
#>  3rd Qu.:2024-02-21  
#>  Max.   :2024-02-21
summary(unemployment_rate)
#>       date             series_id             value        realtime_start      
#>  Min.   :1948-01-01   Length:913         Min.   : 2.500   Min.   :2024-02-21  
#>  1st Qu.:1967-01-01   Class :character   1st Qu.: 4.400   1st Qu.:2024-02-21  
#>  Median :1986-01-01   Mode  :character   Median : 5.500   Median :2024-02-21  
#>  Mean   :1985-12-31                      Mean   : 5.703   Mean   :2024-02-21  
#>  3rd Qu.:2005-01-01                      3rd Qu.: 6.700   3rd Qu.:2024-02-21  
#>  Max.   :2024-01-01                      Max.   :14.800   Max.   :2024-02-21  
#>   realtime_end       
#>  Min.   :2024-02-21  
#>  1st Qu.:2024-02-21  
#>  Median :2024-02-21  
#>  Mean   :2024-02-21  
#>  3rd Qu.:2024-02-21  
#>  Max.   :2024-02-21

ggplot(icnsa, aes(x = date, y = value)) +
  geom_line() +
  labs(title = "Claims",
       x = "Year",
       y = "Number")

ggplot(unemployment_rate, aes(x = date, y = value)) +
  geom_line() +
  labs(title = "Unemployed ",
       x = "Year",
       y = "Number")

library(lubridate)
#> 
#> Attaching package: 'lubridate'
#> The following objects are masked from 'package:base':
#> 
#>     date, intersect, setdiff, union

icnsa <- icnsa %>%
  mutate(Year = year(date),
         Month = month(date))

# since unemployement data is monthly converting icnsa to monthly using mean 
icnsa_monthly <- icnsa %>%
  group_by(Month, Year) %>%
  summarise(ICNSA = mean(value, na.rm = TRUE))
#> `summarise()` has grouped output by 'Month'. You can override using the
#> `.groups` argument.

unemployment_mrate <- unemployment_rate %>%
  mutate(Year = year(date), Month = month(date))

# Merge the datasets by matching months
merged_data <- merge(icnsa_monthly, unemployment_mrate, by = c("Year", "Month"), all = TRUE)

merged_data <- na.omit(merged_data)

# Compute correlation
correlation <- cor(merged_data$ICNSA, merged_data$value)

cat("correlation is:",correlation)
#> correlation is: 0.5061069

library(forecast)
library(tseries)

icsna_ts <- ts(merged_data$ICNSA, frequency = 12, start = c(min(merged_data$Year), 1))
adf_result_icsna <- adf.test(icsna_ts)
#> Warning in adf.test(icsna_ts): p-value smaller than printed p-value
adf_result_icsna
#> 
#>  Augmented Dickey-Fuller Test
#> 
#> data:  icsna_ts
#> Dickey-Fuller = -6.0879, Lag order = 8, p-value = 0.01
#> alternative hypothesis: stationary
print (adf_result_icsna)
#> 
#>  Augmented Dickey-Fuller Test
#> 
#> data:  icsna_ts
#> Dickey-Fuller = -6.0879, Lag order = 8, p-value = 0.01
#> alternative hypothesis: stationary
covariate_ts <- ts(merged_data$value, frequency = 12, start = c(min(merged_data$Year), 1))
adf_result_covariate <- adf.test(covariate_ts)

print (adf_result_covariate)
#> 
#>  Augmented Dickey-Fuller Test
#> 
#> data:  covariate_ts
#> Dickey-Fuller = -3.1865, Lag order = 8, p-value = 0.09025
#> alternative hypothesis: stationary

final_model <- auto.arima(icsna_ts, xreg = covariate_ts)

summary(final_model)
#> Series: icsna_ts 
#> Regression with ARIMA(3,1,4)(0,0,2)[12] errors 
#> 
#> Coefficients:
#>           ar1      ar2     ar3     ma1     ma2      ma3      ma4    sma1
#>       -1.5619  -0.7586  0.0267  1.6285  0.2715  -0.9754  -0.5042  0.2090
#> s.e.   0.2091   0.1527  0.0762  0.2049  0.1690   0.1395   0.1036  0.0418
#>         sma2      drift        xreg
#>       0.1136    47.5389  195093.668
#> s.e.  0.0376  2453.2302    9553.436
#> 
#> sigma^2 = 1.29e+10:  log likelihood = -8927.72
#> AIC=17879.43   AICc=17879.9   BIC=17933.77
#> 
#> Training set error measures:
#>                     ME     RMSE      MAE        MPE     MAPE      MASE
#> Training set -114.6615 112587.9 57531.23 -0.3778597 15.14741 0.6172634
#>                      ACF1
#> Training set 0.0001024701

checkresiduals(final_model)

#> 
#>  Ljung-Box test
#> 
#> data:  Residuals from Regression with ARIMA(3,1,4)(0,0,2)[12] errors
#> Q* = 20.677, df = 15, p-value = 0.1475
#> 
#> Model df: 9.   Total lags used: 24

forecast_values <- forecast(final_model, xreg = covariate_ts, h=1)

single_forecast <- forecast_values$mean[1]

cat ("Next predicted value is ", single_forecast)
#> Next predicted value is  296001.5

^{Created on 2024-02-21 with reprex v2.1.0} Mentioned views and infernces in the pdf attached

[satyamti1250]

HW2 from UB learns

library(dplyr)
#> 
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#> 
#>     filter, lag
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, setequal, union
library(fredr)
library(ggplot2)
library(forecast)
#> Registered S3 method overwritten by 'quantmod':
#>   method            from
#>   as.zoo.data.frame zoo
library(tseries)
library(urca)
library(tidyverse)
library(readxl)
library(forecast)

fredr_set_key("619954596c335c6cd3c4fc1f7a346118")

icnsa <- fredr(series_id = "ICNSA") 

icnsa$date <- as.Date(icnsa$date)
ggplot(icnsa, aes(x = date, y = value)) +
  geom_line() +
  labs(title = "Claims Original ",
       x = "Year",
       y = "Number")

start_date <- as.Date("2020-03-01")
end_date <- as.Date("2021-06-30")

ggplot(icnsa, aes(x = date, y = value)) +
  geom_line() +
  geom_vline(xintercept = as.numeric(start_date), linetype = "dashed", color = "red") +
  geom_vline(xintercept = as.numeric(end_date), linetype = "dashed", color = "red") +
  labs(title = "Claims Marking the Covid period ",
       x = "Year",
       y = "Number")

#Filter covid data out 
non_covid_data <- icnsa %>%
  filter(date < start_date | date > end_date)

#Fitted spline on non-covid data 
spline_fit <- smooth.spline(x = as.numeric(non_covid_data$date), y = non_covid_data$value,lambda = 0.7)

#filtere covid set 
covid_period_data <- icnsa %>%
  filter(date >= start_date & date <= end_date)

#impute new values 
imputed_values <- predict(spline_fit, x = as.numeric(covid_period_data$date))

covid_period_data$value <- imputed_values$y

#new values replacing covid values with imputed values
updated_icnsa_data <- bind_rows(non_covid_data, imputed_values)

updated_icnsa_data <- updated_icnsa_data %>%
  filter(date < Sys.Date())

ggplot(updated_icnsa_data, aes(x = date, y = value)) +
  geom_line() +
  labs(title = "Claims",
       x = "Year",
       y = "Number")

ts_data <- ts(updated_icnsa_data$value, frequency = 12)

hwm <- HoltWinters(ts_data, seasonal = "multiplicative")
f_hwm <- forecast(hwm, h = 1)
print(f_hwm)
#>         Point Forecast    Lo 80    Hi 80    Lo 95    Hi 95
#> Sep 243       210180.3 155439.7 264920.9 126461.8 293898.8

hwa <- HoltWinters(ts_data, seasonal = "additive")
f_hwa <- forecast(hwa, h = 1)
print(f_hwa)
#>         Point Forecast    Lo 80    Hi 80    Lo 95    Hi 95
#> Sep 243       212419.1 145114.7 279723.5 109485.9 315352.3

^{Created on 2024-02-26 with reprex v2.1.0}

[jlivsey]

Why did you set frequency = 12 ? This is weekly data.

[satyamti1250]

library(dplyr)
#> 
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#> 
#>     filter, lag
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, setequal, union
library(fredr)
library(ggplot2)
library(forecast)
#> Registered S3 method overwritten by 'quantmod':
#>   method            from
#>   as.zoo.data.frame zoo
library(tseries)
library(urca)
library(tidyverse)
library(readxl)
library(forecast)
library(dlm)
#> 
#> Attaching package: 'dlm'
#> The following object is masked from 'package:ggplot2':
#> 
#>     %+%

fredr_set_key("619954596c335c6cd3c4fc1f7a346118")

icnsa <- fredr(series_id = "ICNSA") 

icnsa$date <- as.Date(icnsa$date)
ggplot(icnsa, aes(x = date, y = value)) +
  geom_line() +
  labs(title = "Claims Original ",
       x = "Year",
       y = "Number")

start_date <- as.Date("2020-03-01")
end_date <- as.Date("2021-06-30")

ggplot(icnsa, aes(x = date, y = value)) +
  geom_line() +
  geom_vline(xintercept = as.numeric(start_date), linetype = "dashed", color = "red") +
  geom_vline(xintercept = as.numeric(end_date), linetype = "dashed", color = "red") +
  labs(title = "Claims Marking the Covid period ",
       x = "Year",
       y = "Number")

start_date <- as.Date("2020-03-01")
end_date <- as.Date("2021-06-30")

covid_period_data <- icnsa %>%
  filter(date >= start_date & date <= end_date)

non_covid_data <- icnsa %>%
  filter(date < start_date | date > end_date)

warm_up_start_date <- as.Date("2020-01-01") 

warm_up_data <- icnsa %>%
  filter(date >= warm_up_start_date & date < start_date)

combined_data <- bind_rows(warm_up_data, covid_period_data)

y <- covid_period_data$value

buildModel <- function() {
  dV_estimate <- var(non_covid_data$value)
  dW_estimate <- 2500000  

  dlmModPoly(order = 1, dV = dV_estimate, dW = dW_estimate)
}

mod_fitted <- buildModel() 

fit <- dlmFilter(combined_data$value, mod_fitted)

smoothed <- dlmSmooth(fit)

smoothed_estimates <- tail(smoothed$s[-1], n = nrow(covid_period_data))

icnsa_smoothed <- icnsa
icnsa_smoothed$value[icnsa$date >= start_date & icnsa$date <= end_date] <- smoothed_estimates

icnsa_smoothed$date <- as.Date(icnsa$date)
ggplot(icnsa_smoothed, aes(x = date, y = value)) +
  geom_line() +
  labs(title = "Claims Smooth  ",
       x = "Year",
       y = "Number")

library(dlm)
y_smoothed<- icnsa_smoothed$value
dV_start <- var(diff(y_smoothed))
dW_start <- dV_start / 10 

dS_start <- var(y_smoothed) / 2 

buildModel <- function(parm) {
  dV <- parm[1]
  dW <- parm[2]
  dS <- parm[3]
  trend <- dlmModPoly(order = 2, dV = dV)
  seasonal <- dlmModSeas(frequency = 12, dW = rep(dS, 11))  

  model <- trend + seasonal
  return(model)
}

initial_parms <- c(dV_start, dW_start, dS_start)

# Fit the model
fit <- dlmMLE(y_smoothed, parm = initial_parms, build = buildModel)
mod_fitted <- buildModel(fit$par)

filtered <- dlmFilter(y_smoothed, mod_fitted)
smoothed <- dlmSmooth(filtered)

plot(y_smoothed, type = "l", col = "blue", main = "Original vs. Smoothed Series", xlab = "Time", ylab = "Value")
lines(smoothed$s[,1], col = "red")  # Plotting the first state variable
legend("topright", legend = c("Original", "Smoothed"), col = c("blue", "red"), lty = 1)

forecast_length <- 1  
forecasted <- dlmForecast(filtered, nAhead = forecast_length)

forecasted_mean <- forecasted$a[1]
forecasted_mean
#> [1] 239868

alaska <- fredr(series_id = "AKCCLAIMS")

alaska$date <- as.Date(alaska$date)
alaska$value[is.na(alaska$value)] <- mean(alaska$value, na.rm = TRUE)

y_smoothed_trimmed <- tail(y_smoothed, 1985)

dV_start <- var(diff(y_smoothed))
dW_start <- dV_start / 10 
dS_start <- var(y_smoothed) / 2 
buildModelWithCovariate <- function(parm) {
  dV <- parm[1]
  dW <- parm[2]
  dS <- parm[3]

  trend <- dlmModPoly(order = 2, dV = dV)
  seasonal <- dlmModSeas(frequency = 12, dW = rep(dS, 11))
  covariate <- dlmModReg(alaska$value, dV = dV)

  model <- trend + seasonal + covariate
  return(model)
}

initial_parms_with_covariate <- c(dV_start, dW_start, dS_start)  

fit_with_covariate <- dlmMLE(y_smoothed_trimmed, parm = initial_parms_with_covariate, build = buildModelWithCovariate)
mod_fitted_with_covariate <- buildModelWithCovariate(fit_with_covariate$par)

filtered_with_covariate <- dlmFilter(y_smoothed, mod_fitted_with_covariate)
smoothed_with_covariate <- dlmSmooth(filtered_with_covariate)

library(forecast)

arima_model <- auto.arima(y_smoothed_trimmed, xreg = alaska$value)

forecast_arima <- forecast(arima_model, xreg = 300000, h = 1)
forecast_arima
#>      Point Forecast   Lo 80   Hi 80   Lo 95   Hi 95
#> 1986        2152040 2091898 2212182 2060061 2244020

^{Created on 2024-03-07 with reprex v2.1.0}

[satyamti1250]

1- Read the data. 2- Visualized the plot and marked covid dates. 3- I tried to capture the variance of non covid data in dv for dw I was getting very bad results with small values so tried bigger values selected the one which gave good results. Also the initial values I was getting were not very good so I used a small warm up period for my Kalman filter. used it from Jan-2020 and then discarded the initial values from the warm up period. The imputed values are better than the ones from previous spline imputation. 4- Fitted the whole new data in the structured model and smoothened the whole series, got a forecast 5- Fitted the covariate and got a forecast.

[satyamti1250]

Series 1 - Textile products value of shipments

This is my primary series.

It depicts the monthly value of shipments in the textile product industry.

Series 2- Apparel value of shipments

It depicts the monthly value of shipments in the apparel industry.

Series 3- Textile mill of shipments

It depicts the monthly value of shipments in the textile mill industry.

Series 4- Textile products finished inventory

It depicts the monthly value ready industry in the textile product industry.

Part of the economy

My series deals with the clothing industry. My primary series is Textile products shipments values so it should have relationship with Apparel and Textile mills shipment values additionally for the fourth series I have the finished inventory value from the Textile products industry.

Text_Prod_VS = read.csv("/Users/satyamtiwari/Desktop/sem3/T_S/HW4/14SVS.csv")
Text_Prod_FI = read.csv("/Users/satyamtiwari/Desktop/sem3/T_S/HW4/14SFI.csv")
Text_Mill_VS = read.csv("/Users/satyamtiwari/Desktop/sem3/T_S/HW4/13SVS.csv")
Apparel_VS = read.csv("/Users/satyamtiwari/Desktop/sem3/T_S/HW4/15SVS.csv")

tail(Text_Prod_VS)
#>     Period Value
#> 391             
#> 392             
#> 393             
#> 394             
#> 395             
#> 396
head(Text_Prod_FI)
#>     Period Value
#> 1 Jan-1992 1,639
#> 2 Feb-1992 1,641
#> 3 Mar-1992 1,633
#> 4 Apr-1992 1,590
#> 5 May-1992 1,521
#> 6 Jun-1992 1,549
head(Text_Mill_VS)
#>     Period Value
#> 1 Jan-1992 4,324
#> 2 Feb-1992 4,171
#> 3 Mar-1992 4,342
#> 4 Apr-1992 4,427
#> 5 May-1992 4,354
#> 6 Jun-1992 4,432
head(Apparel_VS)
#>     Period Value
#> 1 Jan-1992 4,735
#> 2 Feb-1992 4,753
#> 3 Mar-1992 4,900
#> 4 Apr-1992 4,987
#> 5 May-1992 5,027
#> 6 Jun-1992 5,223

library(ggplot2)
library(zoo) 
#> 
#> Attaching package: 'zoo'
#> The following objects are masked from 'package:base':
#> 
#>     as.Date, as.Date.numeric

library(dplyr) 
#> 
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#> 
#>     filter, lag
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, setequal, union

convert_dates <- function(date_str) {
  as.Date(zoo::as.yearmon(date_str, "%b-%Y"), frac = 1)
}

convert_values <- function(value_str) {
  as.numeric(gsub(",", "", value_str))
}

Text_Prod_VS$Date <- convert_dates(Text_Prod_VS$Period) 
Text_Prod_FI$Date <- convert_dates(Text_Prod_FI$Period)
Text_Mill_VS$Date <- convert_dates(Text_Mill_VS$Period)
Apparel_VS$Date <- convert_dates(Apparel_VS$Period)

Text_Prod_VS$Value <- convert_values(Text_Prod_VS$Value) 
Text_Prod_FI$Value <- convert_values(Text_Prod_FI$Value)
Text_Mill_VS$Value <- convert_values(Text_Mill_VS$Value)
Apparel_VS$Value <- convert_values(Apparel_VS$Value)

# Combining the datasets
combined_data <- rbind(data.frame(Value = Text_Prod_VS$Value, Date = Text_Prod_VS$Date, Series = 'Textile Products Shipments'),
                       data.frame(Value = Text_Prod_FI$Value, Date = Text_Prod_FI$Date, Series = 'Textile Products Finished Inventory'),
                       data.frame(Value = Text_Mill_VS$Value, Date = Text_Mill_VS$Date, Series = 'Textile Mill Shipments'),
                       data.frame(Value = Apparel_VS$Value, Date = Apparel_VS$Date, Series = 'Apparel Shipments'))

ggplot(combined_data, aes(x = Date, y = Value, color = Series)) +
  geom_line() +
  theme_light() +
  scale_x_date(date_breaks = "1 year", date_labels = "%Y") +
  scale_y_continuous(name = "Value", labels = scales::comma) +
  labs(title = "Value of Shipments and Inventory in the Textile and Apparel Industry",
       subtitle = "Monthly Data") +
  theme(axis.text.x = element_text(angle = 45, hjust = 1))
#> Warning: Removed 40 rows containing missing values (`geom_line()`).

Now we do check for trend in the data we see that there is no clear upward or downward trend in the textile production, but it changes its trend along the line

library(ggplot2)
library(zoo)

RollingMean <- rollmean(Text_Prod_VS$Value, 12, fill = NA)

ggplot(Text_Prod_VS, aes(x = Date)) +
  geom_line(aes(y = Value), colour = "blue") +
  geom_line(aes(y = RollingMean), colour = "red") +
  labs(title = "Trend in Textile Products Shipments", x = "Date", y = "Value")
#> Warning: Removed 10 rows containing missing values (`geom_line()`).
#> Warning: Removed 21 rows containing missing values (`geom_line()`).

Now we check for correlation and find that there a great correlation between Apparel_VS and Text_Mill_VS

a good correlation among Text_Mill_VS and Text_Prod_VS, Text_Prod_VS and Apparel_VS

a not so good correlation between Text_Prod_FI and the other 3 series, so maybe this 4th series was not a very good idea.

Text_Prod_VS <- na.omit(Text_Prod_VS)
Text_Prod_FI <- na.omit(Text_Prod_FI)
Text_Mill_VS <- na.omit(Text_Mill_VS)
Apparel_VS <- na.omit(Apparel_VS)

data_ts <- ts(data.frame(Text_Prod_VS$Value, Text_Prod_FI$Value, Text_Mill_VS$Value, Apparel_VS$Value), start=c(1992, 1), frequency=12)

cor_matrix_clean <- cor(data_ts) 
print(cor_matrix_clean)
#>                    Text_Prod_VS.Value Text_Prod_FI.Value Text_Mill_VS.Value
#> Text_Prod_VS.Value          1.0000000          0.2216441          0.6436364
#> Text_Prod_FI.Value          0.2216441          1.0000000          0.1577970
#> Text_Mill_VS.Value          0.6436364          0.1577970          1.0000000
#> Apparel_VS.Value            0.6410749          0.1942598          0.9827279
#>                    Apparel_VS.Value
#> Text_Prod_VS.Value        0.6410749
#> Text_Prod_FI.Value        0.1942598
#> Text_Mill_VS.Value        0.9827279
#> Apparel_VS.Value          1.0000000
#
library(tseries)
#> Registered S3 method overwritten by 'quantmod':
#>   method            from
#>   as.zoo.data.frame zoo

now before applying VAR we need to make sure all four of our series are stationary 

adf.test(Text_Prod_VS$Value)
#> 
#>  Augmented Dickey-Fuller Test
#> 
#> data:  Text_Prod_VS$Value
#> Dickey-Fuller = -2.2114, Lag order = 7, p-value = 0.4879
#> alternative hypothesis: stationary

#p-value = 0.4434 is the p-value so clearly it is not stationary we will now try to  differentiate and check 

Text_Prod_VS_diff <- diff(Text_Prod_VS$Value)
adf_test_diff <- adf.test(Text_Prod_VS_diff, alternative = "stationary")
#> Warning in adf.test(Text_Prod_VS_diff, alternative = "stationary"): p-value
#> smaller than printed p-value

print(adf_test_diff)
#> 
#>  Augmented Dickey-Fuller Test
#> 
#> data:  Text_Prod_VS_diff
#> Dickey-Fuller = -5.8146, Lag order = 7, p-value = 0.01
#> alternative hypothesis: stationary

adf.test(Text_Prod_FI$Value)
#> 
#>  Augmented Dickey-Fuller Test
#> 
#> data:  Text_Prod_FI$Value
#> Dickey-Fuller = -2.6126, Lag order = 7, p-value = 0.3185
#> alternative hypothesis: stationary

#p-value = 0.3185 is the p-value so clearly it is not stationary we will now try to  differentiate and check 

Text_Prod_FI_diff <- diff(Text_Prod_FI$Value)
adf_test_diff <- adf.test(Text_Prod_FI_diff, alternative = "stationary")
#> Warning in adf.test(Text_Prod_FI_diff, alternative = "stationary"): p-value
#> smaller than printed p-value

print(adf_test_diff)
#> 
#>  Augmented Dickey-Fuller Test
#> 
#> data:  Text_Prod_FI_diff
#> Dickey-Fuller = -4.8275, Lag order = 7, p-value = 0.01
#> alternative hypothesis: stationary

adf.test(Text_Mill_VS$Value)
#> 
#>  Augmented Dickey-Fuller Test
#> 
#> data:  Text_Mill_VS$Value
#> Dickey-Fuller = -2.0483, Lag order = 7, p-value = 0.5568
#> alternative hypothesis: stationary

#p-value = 0.5568 is the p-value so clearly it is not stationary we will now try to  differentiate and check 

Text_Mill_VS_diff <- diff(Text_Mill_VS$Value)
adf_test_diff <- adf.test(Text_Mill_VS_diff, alternative = "stationary")
#> Warning in adf.test(Text_Mill_VS_diff, alternative = "stationary"): p-value
#> smaller than printed p-value

print(adf_test_diff)
#> 
#>  Augmented Dickey-Fuller Test
#> 
#> data:  Text_Mill_VS_diff
#> Dickey-Fuller = -6.5932, Lag order = 7, p-value = 0.01
#> alternative hypothesis: stationary

adf.test(Apparel_VS$Value)
#> 
#>  Augmented Dickey-Fuller Test
#> 
#> data:  Apparel_VS$Value
#> Dickey-Fuller = -0.68814, Lag order = 7, p-value = 0.9712
#> alternative hypothesis: stationary

#p-value = 0.9712 is the p-value so clearly it is not stationary we will now try to  differentiate and check 

Apparel_VS_diff <- diff(Apparel_VS$Value)
adf_test_diff <- adf.test(Apparel_VS_diff, alternative = "stationary")
#> Warning in adf.test(Apparel_VS_diff, alternative = "stationary"): p-value
#> smaller than printed p-value

print(adf_test_diff)
#> 
#>  Augmented Dickey-Fuller Test
#> 
#> data:  Apparel_VS_diff
#> Dickey-Fuller = -5.664, Lag order = 7, p-value = 0.01
#> alternative hypothesis: stationary

so differencing once resolves our issue and all 4 of our series are now stationary 

library(vars)
#> Loading required package: MASS
#> 
#> Attaching package: 'MASS'
#> The following object is masked from 'package:dplyr':
#> 
#>     select
#> Loading required package: strucchange
#> Loading required package: sandwich
#> Loading required package: urca
#> Loading required package: lmtest

data_clean <- ts(data.frame(Text_Prod_VS_diff, Text_Prod_FI_diff, Text_Mill_VS_diff, Apparel_VS_diff ), start=c(1992, 1), frequency=12)

VAR1_model <- VAR(data_clean, p=1)
summary(VAR1_model)
#> 
#> VAR Estimation Results:
#> ========================= 
#> Endogenous variables: Text_Prod_VS_diff, Text_Prod_FI_diff, Text_Mill_VS_diff, Apparel_VS_diff 
#> Deterministic variables: const 
#> Sample size: 384 
#> Log Likelihood: -8393.277 
#> Roots of the characteristic polynomial:
#> 0.3566 0.3341 0.3341 0.1667
#> Call:
#> VAR(y = data_clean, p = 1)
#> 
#> 
#> Estimation results for equation Text_Prod_VS_diff: 
#> ================================================== 
#> Text_Prod_VS_diff = Text_Prod_VS_diff.l1 + Text_Prod_FI_diff.l1 + Text_Mill_VS_diff.l1 + Apparel_VS_diff.l1 + const 
#> 
#>                       Estimate Std. Error t value Pr(>|t|)    
#> Text_Prod_VS_diff.l1 -0.231726   0.052762  -4.392 1.46e-05 ***
#> Text_Prod_FI_diff.l1  0.158763   0.092230   1.721    0.086 .  
#> Text_Mill_VS_diff.l1  0.034980   0.037241   0.939    0.348    
#> Apparel_VS_diff.l1   -0.001025   0.028652  -0.036    0.971    
#> const                 0.806526   2.839823   0.284    0.777    
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> 
#> Residual standard error: 55.26 on 379 degrees of freedom
#> Multiple R-Squared: 0.05815, Adjusted R-squared: 0.04821 
#> F-statistic:  5.85 on 4 and 379 DF,  p-value: 0.000141 
#> 
#> 
#> Estimation results for equation Text_Prod_FI_diff: 
#> ================================================== 
#> Text_Prod_FI_diff = Text_Prod_VS_diff.l1 + Text_Prod_FI_diff.l1 + Text_Mill_VS_diff.l1 + Apparel_VS_diff.l1 + const 
#> 
#>                       Estimate Std. Error t value Pr(>|t|)    
#> Text_Prod_VS_diff.l1  0.049657   0.027449   1.809   0.0712 .  
#> Text_Prod_FI_diff.l1  0.349064   0.047983   7.275 2.01e-12 ***
#> Text_Mill_VS_diff.l1 -0.036987   0.019375  -1.909   0.0570 .  
#> Apparel_VS_diff.l1    0.006125   0.014907   0.411   0.6814    
#> const                -0.445081   1.477435  -0.301   0.7634    
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> 
#> Residual standard error: 28.75 on 379 degrees of freedom
#> Multiple R-Squared: 0.1314,  Adjusted R-squared: 0.1223 
#> F-statistic: 14.34 on 4 and 379 DF,  p-value: 6.566e-11 
#> 
#> 
#> Estimation results for equation Text_Mill_VS_diff: 
#> ================================================== 
#> Text_Mill_VS_diff = Text_Prod_VS_diff.l1 + Text_Prod_FI_diff.l1 + Text_Mill_VS_diff.l1 + Apparel_VS_diff.l1 + const 
#> 
#>                      Estimate Std. Error t value Pr(>|t|)    
#> Text_Prod_VS_diff.l1  0.21444    0.07391   2.901  0.00393 ** 
#> Text_Prod_FI_diff.l1  0.07146    0.12920   0.553  0.58049    
#> Text_Mill_VS_diff.l1 -0.28268    0.05217  -5.419 1.07e-07 ***
#> Apparel_VS_diff.l1   -0.04545    0.04014  -1.132  0.25819    
#> const                -7.72508    3.97805  -1.942  0.05289 .  
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> 
#> Residual standard error: 77.41 on 379 degrees of freedom
#> Multiple R-Squared: 0.08689, Adjusted R-squared: 0.07725 
#> F-statistic: 9.016 on 4 and 379 DF,  p-value: 5.777e-07 
#> 
#> 
#> Estimation results for equation Apparel_VS_diff: 
#> ================================================ 
#> Apparel_VS_diff = Text_Prod_VS_diff.l1 + Text_Prod_FI_diff.l1 + Text_Mill_VS_diff.l1 + Apparel_VS_diff.l1 + const 
#> 
#>                       Estimate Std. Error t value Pr(>|t|)    
#> Text_Prod_VS_diff.l1  -0.02605    0.09482  -0.275   0.7837    
#> Text_Prod_FI_diff.l1   0.08767    0.16575   0.529   0.5972    
#> Text_Mill_VS_diff.l1   0.03784    0.06693   0.565   0.5722    
#> Apparel_VS_diff.l1    -0.31088    0.05149  -6.037 3.73e-09 ***
#> const                -13.14700    5.10346  -2.576   0.0104 *  
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> 
#> Residual standard error: 99.31 on 379 degrees of freedom
#> Multiple R-Squared: 0.09477, Adjusted R-squared: 0.08522 
#> F-statistic:  9.92 on 4 and 379 DF,  p-value: 1.212e-07 
#> 
#> 
#> 
#> Covariance matrix of residuals:
#>                   Text_Prod_VS_diff Text_Prod_FI_diff Text_Mill_VS_diff
#> Text_Prod_VS_diff           3053.99            -39.02           1403.10
#> Text_Prod_FI_diff            -39.02            826.61             52.54
#> Text_Mill_VS_diff           1403.10             52.54           5992.72
#> Apparel_VS_diff             1309.15            149.28           2055.79
#>                   Apparel_VS_diff
#> Text_Prod_VS_diff          1309.1
#> Text_Prod_FI_diff           149.3
#> Text_Mill_VS_diff          2055.8
#> Apparel_VS_diff            9863.1
#> 
#> Correlation matrix of residuals:
#>                   Text_Prod_VS_diff Text_Prod_FI_diff Text_Mill_VS_diff
#> Text_Prod_VS_diff           1.00000          -0.02456           0.32798
#> Text_Prod_FI_diff          -0.02456           1.00000           0.02361
#> Text_Mill_VS_diff           0.32798           0.02361           1.00000
#> Apparel_VS_diff             0.23853           0.05228           0.26740
#>                   Apparel_VS_diff
#> Text_Prod_VS_diff         0.23853
#> Text_Prod_FI_diff         0.05228
#> Text_Mill_VS_diff         0.26740
#> Apparel_VS_diff           1.00000

VARp_model <- VARselect(data_clean, lag.max=20, type="both")$selection["AIC(n)"]
VARp_best_model <- VAR(data_clean, p=VARp_model)
summary(VARp_best_model)
#> 
#> VAR Estimation Results:
#> ========================= 
#> Endogenous variables: Text_Prod_VS_diff, Text_Prod_FI_diff, Text_Mill_VS_diff, Apparel_VS_diff 
#> Deterministic variables: const 
#> Sample size: 381 
#> Log Likelihood: -8246.913 
#> Roots of the characteristic polynomial:
#> 0.8612 0.6762 0.6762 0.6524 0.605 0.605 0.5987 0.5664 0.5664 0.5414 0.5414 0.5074 0.5074 0.3799 0.3799 0.1637
#> Call:
#> VAR(y = data_clean, p = VARp_model)
#> 
#> 
#> Estimation results for equation Text_Prod_VS_diff: 
#> ================================================== 
#> Text_Prod_VS_diff = Text_Prod_VS_diff.l1 + Text_Prod_FI_diff.l1 + Text_Mill_VS_diff.l1 + Apparel_VS_diff.l1 + Text_Prod_VS_diff.l2 + Text_Prod_FI_diff.l2 + Text_Mill_VS_diff.l2 + Apparel_VS_diff.l2 + Text_Prod_VS_diff.l3 + Text_Prod_FI_diff.l3 + Text_Mill_VS_diff.l3 + Apparel_VS_diff.l3 + Text_Prod_VS_diff.l4 + Text_Prod_FI_diff.l4 + Text_Mill_VS_diff.l4 + Apparel_VS_diff.l4 + const 
#> 
#>                       Estimate Std. Error t value Pr(>|t|)    
#> Text_Prod_VS_diff.l1 -0.243802   0.055240  -4.414 1.34e-05 ***
#> Text_Prod_FI_diff.l1  0.159719   0.103796   1.539  0.12473    
#> Text_Mill_VS_diff.l1  0.037437   0.039755   0.942  0.34697    
#> Apparel_VS_diff.l1   -0.023480   0.030204  -0.777  0.43743    
#> Text_Prod_VS_diff.l2 -0.080844   0.057874  -1.397  0.16329    
#> Text_Prod_FI_diff.l2 -0.099758   0.104902  -0.951  0.34225    
#> Text_Mill_VS_diff.l2 -0.017690   0.041059  -0.431  0.66684    
#> Apparel_VS_diff.l2   -0.007022   0.031591  -0.222  0.82421    
#> Text_Prod_VS_diff.l3  0.150621   0.058004   2.597  0.00979 ** 
#> Text_Prod_FI_diff.l3  0.100410   0.104141   0.964  0.33560    
#> Text_Mill_VS_diff.l3  0.014339   0.041086   0.349  0.72730    
#> Apparel_VS_diff.l3    0.047203   0.031280   1.509  0.13215    
#> Text_Prod_VS_diff.l4  0.003493   0.057316   0.061  0.95143    
#> Text_Prod_FI_diff.l4 -0.028336   0.102702  -0.276  0.78278    
#> Text_Mill_VS_diff.l4  0.057295   0.038633   1.483  0.13892    
#> Apparel_VS_diff.l4    0.025735   0.029723   0.866  0.38715    
#> const                 0.768449   2.906277   0.264  0.79161    
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> 
#> Residual standard error: 53.65 on 364 degrees of freedom
#> Multiple R-Squared: 0.1265,  Adjusted R-squared: 0.08811 
#> F-statistic: 3.295 on 16 and 364 DF,  p-value: 2.159e-05 
#> 
#> 
#> Estimation results for equation Text_Prod_FI_diff: 
#> ================================================== 
#> Text_Prod_FI_diff = Text_Prod_VS_diff.l1 + Text_Prod_FI_diff.l1 + Text_Mill_VS_diff.l1 + Apparel_VS_diff.l1 + Text_Prod_VS_diff.l2 + Text_Prod_FI_diff.l2 + Text_Mill_VS_diff.l2 + Apparel_VS_diff.l2 + Text_Prod_VS_diff.l3 + Text_Prod_FI_diff.l3 + Text_Mill_VS_diff.l3 + Apparel_VS_diff.l3 + Text_Prod_VS_diff.l4 + Text_Prod_FI_diff.l4 + Text_Mill_VS_diff.l4 + Apparel_VS_diff.l4 + const 
#> 
#>                       Estimate Std. Error t value Pr(>|t|)    
#> Text_Prod_VS_diff.l1  0.032406   0.027297   1.187 0.235935    
#> Text_Prod_FI_diff.l1  0.172298   0.051292   3.359 0.000864 ***
#> Text_Mill_VS_diff.l1 -0.024452   0.019645  -1.245 0.214047    
#> Apparel_VS_diff.l1    0.009109   0.014926   0.610 0.542049    
#> Text_Prod_VS_diff.l2 -0.016073   0.028599  -0.562 0.574458    
#> Text_Prod_FI_diff.l2  0.224758   0.051838   4.336 1.88e-05 ***
#> Text_Mill_VS_diff.l2  0.013679   0.020290   0.674 0.500609    
#> Apparel_VS_diff.l2    0.031818   0.015611   2.038 0.042250 *  
#> Text_Prod_VS_diff.l3  0.043124   0.028663   1.505 0.133316    
#> Text_Prod_FI_diff.l3  0.072484   0.051462   1.408 0.159842    
#> Text_Mill_VS_diff.l3  0.009392   0.020303   0.463 0.643953    
#> Apparel_VS_diff.l3    0.021418   0.015457   1.386 0.166709    
#> Text_Prod_VS_diff.l4  0.012191   0.028323   0.430 0.667143    
#> Text_Prod_FI_diff.l4  0.170684   0.050751   3.363 0.000852 ***
#> Text_Mill_VS_diff.l4  0.010425   0.019091   0.546 0.585357    
#> Apparel_VS_diff.l4    0.013754   0.014688   0.936 0.349682    
#> const                 0.967188   1.436164   0.673 0.501087    
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> 
#> Residual standard error: 26.51 on 364 degrees of freedom
#> Multiple R-Squared: 0.2774,  Adjusted R-squared: 0.2457 
#> F-statistic: 8.735 on 16 and 364 DF,  p-value: < 2.2e-16 
#> 
#> 
#> Estimation results for equation Text_Mill_VS_diff: 
#> ================================================== 
#> Text_Mill_VS_diff = Text_Prod_VS_diff.l1 + Text_Prod_FI_diff.l1 + Text_Mill_VS_diff.l1 + Apparel_VS_diff.l1 + Text_Prod_VS_diff.l2 + Text_Prod_FI_diff.l2 + Text_Mill_VS_diff.l2 + Apparel_VS_diff.l2 + Text_Prod_VS_diff.l3 + Text_Prod_FI_diff.l3 + Text_Mill_VS_diff.l3 + Apparel_VS_diff.l3 + Text_Prod_VS_diff.l4 + Text_Prod_FI_diff.l4 + Text_Mill_VS_diff.l4 + Apparel_VS_diff.l4 + const 
#> 
#>                       Estimate Std. Error t value Pr(>|t|)    
#> Text_Prod_VS_diff.l1  0.267945   0.077103   3.475 0.000572 ***
#> Text_Prod_FI_diff.l1  0.025166   0.144877   0.174 0.862195    
#> Text_Mill_VS_diff.l1 -0.306465   0.055489  -5.523 6.35e-08 ***
#> Apparel_VS_diff.l1   -0.065186   0.042159  -1.546 0.122922    
#> Text_Prod_VS_diff.l2  0.096778   0.080780   1.198 0.231678    
#> Text_Prod_FI_diff.l2 -0.195889   0.146421  -1.338 0.181781    
#> Text_Mill_VS_diff.l2 -0.128491   0.057310  -2.242 0.025561 *  
#> Apparel_VS_diff.l2    0.054316   0.044094   1.232 0.218808    
#> Text_Prod_VS_diff.l3  0.313273   0.080961   3.869 0.000129 ***
#> Text_Prod_FI_diff.l3  0.075738   0.145360   0.521 0.602657    
#> Text_Mill_VS_diff.l3  0.054167   0.057348   0.945 0.345529    
#> Apparel_VS_diff.l3   -0.001703   0.043660  -0.039 0.968903    
#> Text_Prod_VS_diff.l4 -0.016957   0.080001  -0.212 0.832259    
#> Text_Prod_FI_diff.l4  0.205927   0.143351   1.437 0.151712    
#> Text_Mill_VS_diff.l4  0.069084   0.053923   1.281 0.200958    
#> Apparel_VS_diff.l4    0.021785   0.041487   0.525 0.599836    
#> const                -7.968639   4.056558  -1.964 0.050246 .  
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> 
#> Residual standard error: 74.88 on 364 degrees of freedom
#> Multiple R-Squared: 0.1646,  Adjusted R-squared: 0.1279 
#> F-statistic: 4.482 on 16 and 364 DF,  p-value: 3.756e-08 
#> 
#> 
#> Estimation results for equation Apparel_VS_diff: 
#> ================================================ 
#> Apparel_VS_diff = Text_Prod_VS_diff.l1 + Text_Prod_FI_diff.l1 + Text_Mill_VS_diff.l1 + Apparel_VS_diff.l1 + Text_Prod_VS_diff.l2 + Text_Prod_FI_diff.l2 + Text_Mill_VS_diff.l2 + Apparel_VS_diff.l2 + Text_Prod_VS_diff.l3 + Text_Prod_FI_diff.l3 + Text_Mill_VS_diff.l3 + Apparel_VS_diff.l3 + Text_Prod_VS_diff.l4 + Text_Prod_FI_diff.l4 + Text_Mill_VS_diff.l4 + Apparel_VS_diff.l4 + const 
#> 
#>                       Estimate Std. Error t value Pr(>|t|)    
#> Text_Prod_VS_diff.l1   0.07763    0.10010   0.776  0.43854    
#> Text_Prod_FI_diff.l1  -0.03473    0.18809  -0.185  0.85362    
#> Text_Mill_VS_diff.l1  -0.01290    0.07204  -0.179  0.85801    
#> Apparel_VS_diff.l1    -0.34978    0.05473  -6.391 5.06e-10 ***
#> Text_Prod_VS_diff.l2   0.30414    0.10487   2.900  0.00396 ** 
#> Text_Prod_FI_diff.l2  -0.17678    0.19010  -0.930  0.35302    
#> Text_Mill_VS_diff.l2  -0.08086    0.07440  -1.087  0.27785    
#> Apparel_VS_diff.l2    -0.09836    0.05725  -1.718  0.08662 .  
#> Text_Prod_VS_diff.l3   0.20920    0.10511   1.990  0.04731 *  
#> Text_Prod_FI_diff.l3   0.54317    0.18872   2.878  0.00424 ** 
#> Text_Mill_VS_diff.l3  -0.04616    0.07445  -0.620  0.53570    
#> Apparel_VS_diff.l3    -0.02891    0.05668  -0.510  0.61031    
#> Text_Prod_VS_diff.l4  -0.02794    0.10386  -0.269  0.78811    
#> Text_Prod_FI_diff.l4  -0.05286    0.18611  -0.284  0.77654    
#> Text_Mill_VS_diff.l4   0.11803    0.07001   1.686  0.09266 .  
#> Apparel_VS_diff.l4    -0.05399    0.05386  -1.002  0.31685    
#> const                -16.82112    5.26654  -3.194  0.00153 ** 
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> 
#> Residual standard error: 97.22 on 364 degrees of freedom
#> Multiple R-Squared: 0.1593,  Adjusted R-squared: 0.1224 
#> F-statistic: 4.312 on 16 and 364 DF,  p-value: 9.455e-08 
#> 
#> 
#> 
#> Covariance matrix of residuals:
#>                   Text_Prod_VS_diff Text_Prod_FI_diff Text_Mill_VS_diff
#> Text_Prod_VS_diff           2878.32            -55.06              1150
#> Text_Prod_FI_diff            -55.06            702.87               -27
#> Text_Mill_VS_diff           1150.42            -27.00              5608
#> Apparel_VS_diff             1154.77            178.39              1808
#>                   Apparel_VS_diff
#> Text_Prod_VS_diff          1154.8
#> Text_Prod_FI_diff           178.4
#> Text_Mill_VS_diff          1807.9
#> Apparel_VS_diff            9451.8
#> 
#> Correlation matrix of residuals:
#>                   Text_Prod_VS_diff Text_Prod_FI_diff Text_Mill_VS_diff
#> Text_Prod_VS_diff           1.00000          -0.03871            0.2863
#> Text_Prod_FI_diff          -0.03871           1.00000           -0.0136
#> Text_Mill_VS_diff           0.28635          -0.01360            1.0000
#> Apparel_VS_diff             0.22139           0.06921            0.2483
#>                   Apparel_VS_diff
#> Text_Prod_VS_diff         0.22139
#> Text_Prod_FI_diff         0.06921
#> Text_Mill_VS_diff         0.24832
#> Apparel_VS_diff           1.00000

##comparing the 2 models I can see that Log Likelihood is better for varp also R-squared is better for varp.Both models show some correlation between residuals but comparing the two, based on the higher log likelihood,  higher  R-squared values, and the greater number of significant predictors, the var(p) model seems better. 

forecast_VAR1 <- forecast(VAR1_model, h=1)
#> Error in forecast(VAR1_model, h = 1): could not find function "forecast"
forecast_VARp <- forecast(VARp_best_model, h=1)
#> Error in forecast(VARp_best_model, h = 1): could not find function "forecast"

last_value_Text_Prod_VS<- tail(Text_Prod_VS$Value, 1)

mean_forecast_var1_Text_Prod_VS_diff <- forecast_VAR1$forecast$Text_Prod_VS_diff$mean
#> Error in eval(expr, envir, enclos): object 'forecast_VAR1' not found
mean_forecast_varp_Text_Prod_VS_diff <- forecast_VARp$forecast$Text_Prod_VS_diff$mean
#> Error in eval(expr, envir, enclos): object 'forecast_VARp' not found

original_forecast_VAR1_Text_Prod_VS <- last_value_Text_Prod_VS + mean_forecast_var1_Text_Prod_VS_diff
#> Error in eval(expr, envir, enclos): object 'mean_forecast_var1_Text_Prod_VS_diff' not found
original_forecast_VARP_Text_Prod_VS <- last_value_Text_Prod_VS + mean_forecast_varp_Text_Prod_VS_diff
#> Error in eval(expr, envir, enclos): object 'mean_forecast_varp_Text_Prod_VS_diff' not found

print("Var1 prediction for textile production value")
#> [1] "Var1 prediction for textile production value"
print(original_forecast_VAR1_Text_Prod_VS)
#> Error in eval(expr, envir, enclos): object 'original_forecast_VAR1_Text_Prod_VS' not found

print("Var(p) prediction for textile production value")
#> [1] "Var(p) prediction for textile production value"
print(original_forecast_VARP_Text_Prod_VS)
#> Error in eval(expr, envir, enclos): object 'original_forecast_VARP_Text_Prod_VS' not found

causality_test_result <- causality(VARp_best_model, cause="Text_Prod_VS_diff")
print(causality_test_result$Granger)
#> 
#>  Granger causality H0: Text_Prod_VS_diff do not Granger-cause
#>  Text_Prod_FI_diff Text_Mill_VS_diff Apparel_VS_diff
#> 
#> data:  VAR object VARp_best_model
#> F-Test = 3.3546, df1 = 12, df2 = 1456, p-value = 7.629e-05

So seeing this we can reject the null hypothesis so my series Textile_Products does contain some information about the other series. 

library(BigVAR)
#> Loading required package: lattice

p_optimal =5
model_spec <- constructModel(data_clean, p = p_optimal, struct = "SparseLag", gran=c(50,10))
ms <- constructModel(data_clean, p = p_optimal, struct = "SparseOO", gran=c(50,10))

results=cv.BigVAR(model_spec)
#> Validation Stage: SparseLag  |                                                                              |                                                                      |   0%  |                                                                              |=                                                                     |   1%  |                                                                              |=                                                                     |   2%  |                                                                              |==                                                                    |   2%  |                                                                              |==                                                                    |   3%  |                                                                              |===                                                                   |   4%  |                    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print(results)
#> *** BIGVAR MODEL Results *** 
#> Structure
#> [1] "SparseLag"
#> Loss 
#> [1] "L2"
#> Forecast Horizon 
#> [1] 1
#> Minnesota VAR
#> [1] FALSE
#> Maximum Lag Order 
#> [1] 5
#> Optimal Lambda 
#> [1] 59490
#> Grid Depth 
#> [1] 50
#> Index of Optimal Lambda 
#> [1] 5
#> Fraction of active coefficients 
#> [1] 0.6432
#> In-Sample Loss
#> [1] 13300
#> BigVAR Out of Sample Loss
#> [1] 6230
#> *** Benchmark Results *** 
#> Conditional Mean Out of Sample Loss
#> [1] 6340
#> AIC Out of Sample Loss
#> [1] 7290
#> BIC Out of Sample Loss
#> [1] 6280
#> RW Out of Sample Loss
#> [1] 12900
plot(results)

results2=cv.BigVAR(ms)
#> Validation Stage: SparseOO  |                                                                              |                                                                      |   0%  |                                                                              |=                                                                     |   1%  |                                                                              |=                                                                     |   2%  |                                                                              |==                                                                    |   2%  |                                                                              |==                                                                    |   3%  |                                                                              |===                                                                   |   4%  |                     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print(results2)
#> *** BIGVAR MODEL Results *** 
#> Structure
#> [1] "SparseOO"
#> Loss 
#> [1] "L2"
#> Forecast Horizon 
#> [1] 1
#> Minnesota VAR
#> [1] FALSE
#> Maximum Lag Order 
#> [1] 5
#> Optimal Lambda 
#> [1] 16.82
#> Grid Depth 
#> [1] 50
#> Index of Optimal Lambda 
#> [1] 10
#> Fraction of active coefficients 
#> [1] 1
#> In-Sample Loss
#> [1] 13200
#> BigVAR Out of Sample Loss
#> [1] 6270
#> *** Benchmark Results *** 
#> Conditional Mean Out of Sample Loss
#> [1] 6340
#> AIC Out of Sample Loss
#> [1] 7290
#> BIC Out of Sample Loss
#> [1] 6280
#> RW Out of Sample Loss
#> [1] 12900
plot(results2)

Comparing SparseLag and SparseOO they have similar loss sparse00 has Fraction of active coefficients as 100% so it is probably overfitting so considering the current state SparseLag seems better. ^{Created on 2024-04-10 with reprex v2.1.0}

[satyamti1250]

library(ggplot2)
Nvidia_share<- read.csv("/Users/satyamtiwari/Desktop/PR/Nvidia_share.csv")
head(Nvidia_share)
#>         Date Close.Last   Volume    Open    High      Low
#> 1 03/19/2024    $893.98 67217130 $867.00 $905.44  $850.10
#> 2 03/18/2024    $884.55 66897590 $903.88 $924.05  $870.85
#> 3 03/15/2024   $878.365 64208620 $869.30 $895.46  $862.57
#> 4 03/14/2024    $879.44 60231820 $895.77 $906.46  $866.00
#> 5 03/13/2024    $908.88 63571290 $910.55 $915.04  $884.35
#> 6 03/12/2024    $919.13 66807520 $880.49 $919.60 $861.501

Nvidia_share$Date <- as.Date(Nvidia_share$Date, format = "%m/%d/%Y")
Nvidia_share$Open <- as.numeric(gsub("\\$", "", Nvidia_share$Open))

ggplot(Nvidia_share, aes(x = Date, y = Open)) +
  geom_line() +
  labs(title = "Claims",
       x = "Year",
       y = "Number")

amd_share<- read.csv("/Users/satyamtiwari/Desktop/PR/amd_share.csv")

amd_share$Date <- as.Date(amd_share$Date, format = "%m/%d/%Y")
amd_share$Open <- as.numeric(gsub("\\$", "", amd_share$Open))

ggplot(amd_share, aes(x = Date, y = Open)) +
  geom_line() +
  labs(title = "Claims",
       x = "Year",
       y = "Number")

merged_data <- merge(Nvidia_share, amd_share, by = "Date")

covid_start_date <- as.Date("2020-03-01")
covid_end_date <- as.Date("2021-03-30")
Bitcoin_bull_run <- as.Date("2017-12-17")
China_ban <- as.Date("2021-06-21")

p1 <- ggplot(merged_data, aes(x = Date)) + 
  geom_line(aes(y = Open.x, color = "NVIDA")) +
  labs(y = "NVIDIA vs AMD Share price", color = "Series") +
  theme_minimal()

p2 <- p1 + geom_line(aes(y = Open.y, color = "AMD"))+geom_vline(xintercept = as.numeric(covid_start_date), linetype = "dashed", color = "red") +geom_vline(xintercept = as.numeric(covid_end_date), linetype = "dashed", color = "red") +geom_vline(xintercept = as.numeric(Bitcoin_bull_run), linetype = "dashed", color = "green") +geom_vline(xintercept = as.numeric(China_ban), linetype = "dashed", color = "black") 

final_plot <- p2 + scale_y_continuous(sec.axis = sec_axis(~., name = "NVIDIA vs AMD Share price"))

print(final_plot)

Markers Green - The Bitcoin Bull run starts Red Line - Start and end of the Covid pandemic Black - China Bans mining of crypto

library(ggplot2)
revenue<- read.csv("/Users/satyamtiwari/Desktop/PR/revenues.csv")
head(revenue)
#>       Date Nvidia_Revenue Amd_Revenue  X X.1 X.2
#> 1  1/31/24       $22,103      $6,168  NA  NA  NA
#> 2 10/31/23       $18,120      $5,800  NA  NA  NA
#> 3  7/31/23       $13,507      $5,359  NA  NA  NA
#> 4  4/30/23        $7,192      $5,353  NA  NA  NA
#> 5  1/31/23        $6,051      $5,599  NA  NA  NA
#> 6 10/31/22        $5,931      $5,565  NA  NA  NA

revenue$Date <- as.Date(revenue$Date, format = "%m/%d/%y")
revenue$Nvidia_Revenue <- as.numeric(gsub(",", "", gsub("\\$", "", revenue$Nvidia_Revenue)))
revenue$Amd_Revenue <- as.numeric(gsub(",", "", gsub("\\$", "", revenue$Amd_Revenue)))

p1 <- ggplot(revenue, aes(x = Date)) + 
  geom_line(aes(y = Nvidia_Revenue, color = "NVIDA")) +
  labs(y = "NVIDIA vs AMD Revenue in Million $", color = "Series") +
  theme_minimal()

p2 <- p1 + geom_line(aes(y = Amd_Revenue, color = "AMD"))+geom_vline(xintercept = as.numeric(covid_start_date), linetype = "dashed", color = "red") +geom_vline(xintercept = as.numeric(covid_end_date), linetype = "dashed", color = "red") +geom_vline(xintercept = as.numeric(Bitcoin_bull_run), linetype = "dashed", color = "green") +geom_vline(xintercept = as.numeric(China_ban), linetype = "dashed", color = "black") 

final_plot <- p2 + scale_y_continuous(sec.axis = sec_axis(~., name = "NVIDIA vs AMD Revenue in Million $"))

print(final_plot)
#> Warning: Removed 2 rows containing missing values (`geom_line()`).
#> Removed 2 rows containing missing values (`geom_line()`).

Markers Green - The Bitcoin Bull run starts Red Line - Start and end of the Covid pandemic Black - China Bans mining of crypto

library(tseries)  
#> Registered S3 method overwritten by 'quantmod':
#>   method            from
#>   as.zoo.data.frame zoo
NV <- ts(Nvidia_share$Open, frequency=365) 
AM <- ts(amd_share$Open, frequency=365) 

NV_adf_result <- adf.test(NV, alternative = "stationary")
#> Warning in adf.test(NV, alternative = "stationary"): p-value smaller than
#> printed p-value
AM_adf_result <- adf.test(AM, alternative = "stationary")
print(NV_adf_result)
#> 
#>  Augmented Dickey-Fuller Test
#> 
#> data:  NV
#> Dickey-Fuller = -6.3817, Lag order = 13, p-value = 0.01
#> alternative hypothesis: stationary
print(AM_adf_result)
#> 
#>  Augmented Dickey-Fuller Test
#> 
#> data:  AM
#> Dickey-Fuller = -3.4419, Lag order = 13, p-value = 0.04788
#> alternative hypothesis: stationary

cor(NV, AM)
#> [1] 0.8939226

data<- ts(data.frame(NV, AM), frequency=365)

library(lmtest)
#> Loading required package: zoo
#> 
#> Attaching package: 'zoo'
#> The following objects are masked from 'package:base':
#> 
#>     as.Date, as.Date.numeric
grangertest(data, order=1)
#> Granger causality test
#> 
#> Model 1: AM ~ Lags(AM, 1:1) + Lags(NV, 1:1)
#> Model 2: AM ~ Lags(AM, 1:1)
#>   Res.Df Df     F Pr(>F)
#> 1   2513                
#> 2   2514 -1 0.011 0.9166

library(vars)
#> Loading required package: MASS
#> Loading required package: strucchange
#> Loading required package: sandwich
#> Loading required package: urca
var_model <- VAR(data, p=12, type="both")
summary(var_model)
#> 
#> VAR Estimation Results:
#> ========================= 
#> Endogenous variables: NV, AM 
#> Deterministic variables: both 
#> Sample size: 2505 
#> Log Likelihood: -12417.018 
#> Roots of the characteristic polynomial:
#> 0.9954 0.9892 0.8265 0.8265 0.8244 0.8097 0.8097 0.7964 0.7964 0.7819 0.7819 0.7408 0.7408 0.7344 0.7344 0.7254 0.7254 0.7193 0.7193 0.7183 0.7183 0.6934 0.2834 0.2834
#> Call:
#> VAR(y = data, p = 12, type = "both")
#> 
#> 
#> Estimation results for equation NV: 
#> =================================== 
#> NV = NV.l1 + AM.l1 + NV.l2 + AM.l2 + NV.l3 + AM.l3 + NV.l4 + AM.l4 + NV.l5 + AM.l5 + NV.l6 + AM.l6 + NV.l7 + AM.l7 + NV.l8 + AM.l8 + NV.l9 + AM.l9 + NV.l10 + AM.l10 + NV.l11 + AM.l11 + NV.l12 + AM.l12 + const + trend 
#> 
#>          Estimate Std. Error t value Pr(>|t|)    
#> NV.l1   0.9777200  0.0284920  34.316  < 2e-16 ***
#> AM.l1  -0.1944993  0.0749753  -2.594 0.009538 ** 
#> NV.l2   0.0079813  0.0392854   0.203 0.839024    
#> AM.l2   0.1313869  0.1060265   1.239 0.215393    
#> NV.l3  -0.0281947  0.0391917  -0.719 0.471960    
#> AM.l3  -0.1430864  0.1056072  -1.355 0.175575    
#> NV.l4   0.0598652  0.0390962   1.531 0.125841    
#> AM.l4   0.2304950  0.1056629   2.181 0.029246 *  
#> NV.l5   0.0244619  0.0366825   0.667 0.504927    
#> AM.l5  -0.0748564  0.1041312  -0.719 0.472291    
#> NV.l6  -0.0878701  0.0353141  -2.488 0.012903 *  
#> AM.l6   0.2647589  0.1022669   2.589 0.009685 ** 
#> NV.l7   0.1392643  0.0350993   3.968 7.46e-05 ***
#> AM.l7  -0.3016037  0.1014831  -2.972 0.002988 ** 
#> NV.l8  -0.0518147  0.0349555  -1.482 0.138386    
#> AM.l8   0.0117976  0.1013141   0.116 0.907309    
#> NV.l9  -0.0458495  0.0348398  -1.316 0.188294    
#> AM.l9   0.0236104  0.1011528   0.233 0.815460    
#> NV.l10  0.0660668  0.0347182   1.903 0.057164 .  
#> AM.l10 -0.0558620  0.1009492  -0.553 0.580062    
#> NV.l11 -0.1707172  0.0345710  -4.938 8.41e-07 ***
#> AM.l11  0.2018303  0.1008654   2.001 0.045503 *  
#> NV.l12  0.0991442  0.0256564   3.864 0.000114 ***
#> AM.l12 -0.0965049  0.0721201  -1.338 0.180982    
#> const   2.3105572  0.7134279   3.239 0.001217 ** 
#> trend  -0.0011102  0.0003584  -3.097 0.001975 ** 
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> 
#> Residual standard error: 5.617 on 2479 degrees of freedom
#> Multiple R-Squared: 0.9983,  Adjusted R-squared: 0.9983 
#> F-statistic: 5.943e+04 on 25 and 2479 DF,  p-value: < 2.2e-16 
#> 
#> 
#> Estimation results for equation AM: 
#> =================================== 
#> AM = NV.l1 + AM.l1 + NV.l2 + AM.l2 + NV.l3 + AM.l3 + NV.l4 + AM.l4 + NV.l5 + AM.l5 + NV.l6 + AM.l6 + NV.l7 + AM.l7 + NV.l8 + AM.l8 + NV.l9 + AM.l9 + NV.l10 + AM.l10 + NV.l11 + AM.l11 + NV.l12 + AM.l12 + const + trend 
#> 
#>          Estimate Std. Error t value Pr(>|t|)    
#> NV.l1   0.0113727  0.0108623   1.047   0.2952    
#> AM.l1   0.9518544  0.0285836  33.301  < 2e-16 ***
#> NV.l2  -0.0198626  0.0149772  -1.326   0.1849    
#> AM.l2   0.0178332  0.0404216   0.441   0.6591    
#> NV.l3   0.0006365  0.0149415   0.043   0.9660    
#> AM.l3   0.0041763  0.0402618   0.104   0.9174    
#> NV.l4   0.0135986  0.0149051   0.912   0.3617    
#> AM.l4   0.0064382  0.0402830   0.160   0.8730    
#> NV.l5   0.0221460  0.0139849   1.584   0.1134    
#> AM.l5  -0.0160912  0.0396991  -0.405   0.6853    
#> NV.l6  -0.0528597  0.0134632  -3.926 8.86e-05 ***
#> AM.l6   0.0923060  0.0389883   2.368   0.0180 *  
#> NV.l7   0.0625901  0.0133813   4.677 3.06e-06 ***
#> AM.l7  -0.0946120  0.0386895  -2.445   0.0145 *  
#> NV.l8  -0.0178955  0.0133265  -1.343   0.1794    
#> AM.l8  -0.0336717  0.0386251  -0.872   0.3834    
#> NV.l9  -0.0098058  0.0132824  -0.738   0.4604    
#> AM.l9   0.0136049  0.0385636   0.353   0.7243    
#> NV.l10 -0.0107292  0.0132360  -0.811   0.4177    
#> AM.l10  0.0595358  0.0384860   1.547   0.1220    
#> NV.l11 -0.0216828  0.0131799  -1.645   0.1001    
#> AM.l11  0.0106257  0.0384540   0.276   0.7823    
#> NV.l12  0.0214904  0.0097813   2.197   0.0281 *  
#> AM.l12 -0.0176267  0.0274951  -0.641   0.5215    
#> const   0.7696165  0.2719880   2.830   0.0047 ** 
#> trend  -0.0003736  0.0001367  -2.734   0.0063 ** 
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> 
#> Residual standard error: 2.141 on 2479 degrees of freedom
#> Multiple R-Squared: 0.9977,  Adjusted R-squared: 0.9977 
#> F-statistic: 4.385e+04 on 25 and 2479 DF,  p-value: < 2.2e-16 
#> 
#> 
#> 
#> Covariance matrix of residuals:
#>        NV    AM
#> NV 31.549 8.598
#> AM  8.598 4.585
#> 
#> Correlation matrix of residuals:
#>        NV     AM
#> NV 1.0000 0.7149
#> AM 0.7149 1.0000

library(vars)
var_model <- VAR(data, p=12, type="both")
irf_results <- irf(var_model, impulse="NV", response="AM", n.ahead=20)
plot(irf_results)

library(urca)
johansen_test <- ca.jo(data, spec = "transitory", type = "eigen", K = 2)
summary(johansen_test)
#> 
#> ###################### 
#> # Johansen-Procedure # 
#> ###################### 
#> 
#> Test type: maximal eigenvalue statistic (lambda max) , with linear trend 
#> 
#> Eigenvalues (lambda):
#> [1] 0.03796007 0.00157393
#> 
#> Values of teststatistic and critical values of test:
#> 
#>           test 10pct  5pct  1pct
#> r <= 1 |  3.96  6.50  8.18 11.65
#> r = 0  | 97.33 12.91 14.90 19.19
#> 
#> Eigenvectors, normalised to first column:
#> (These are the cointegration relations)
#> 
#>           NV.l1     AM.l1
#> NV.l1  1.000000  1.000000
#> AM.l1 -1.621176 -4.513087
#> 
#> Weights W:
#> (This is the loading matrix)
#> 
#>             NV.l1        AM.l1
#> NV.d -0.012316618 0.0012271644
#> AM.d -0.001261921 0.0008388962

Implications Presence of Cointegration: The presence of at least one cointegrating vector implies that despite short-term fluctuations, there exists a stable long-term relationship between NVIDIA and AMD share prices. This can be interpreted as indicating that the stocks move together over the long term, perhaps due to similar market forces affecting them. Strategic Decisions: For strategic decision-making, this could imply that positions in one of these stocks might be hedged by positions in the other, reflecting their long-term linkage. ^{Created on 2024-05-12 with reprex v2.1.0}