jlivsey
commented
7 months ago Please note this does not satisfy the criteria. Specifically that part that says "results visable without downloading"
Open Akshayapeduru opened 7 months ago
jlivsey
commented
7 months ago Please note this does not satisfy the criteria. Specifically that part that says "results visable without downloading"
Akshayapeduru
commented
7 months ago please let me know if i need to upload ipynb file along with the pdf in brightspace.
Akshayapeduru
commented
7 months ago Multiplicative Model - 279634.5811 HW2f- ICNSA_akshayap.pdf
Akshayapeduru
commented
6 months ago Forecast value:369548.6 HW3- akshayap - ICNSA Forecast.pdf
Akshayapeduru
commented
5 months ago library(forecast)
#> Warning: package 'forecast' was built under R version 4.2.3
#> Registered S3 method overwritten by 'quantmod':
#> method from
#> as.zoo.data.frame zoo
library(vars)
#> Warning: package 'vars' was built under R version 4.2.3
#> Loading required package: MASS
#> Loading required package: strucchange
#> Loading required package: zoo
#>
#> Attaching package: 'zoo'
#> The following objects are masked from 'package:base':
#>
#> as.Date, as.Date.numeric
#> Loading required package: sandwich
#> Loading required package: urca
#> Loading required package: lmtest
library(tseries)
library(readxl)
library(ggplot2)
All_Houses <- read.csv("/Users/akshayapeduru/Downloads/All_Houses.csv", skip = 7)
print(head(All_Houses))
#> Period Value
#> 1 Jan-1963 591
#> 2 Feb-1963 464
#> 3 Mar-1963 461
#> 4 Apr-1963 605
#> 5 May-1963 586
#> 6 Jun-1963 526
Houses_Not_Started <- read.csv("/Users/akshayapeduru/Downloads/Houses_Not_Started.csv", skip = 7)
print(head(Houses_Not_Started))
#> Period Value
#> 1 Jan-1963 NA
#> 2 Feb-1963 NA
#> 3 Mar-1963 NA
#> 4 Apr-1963 NA
#> 5 May-1963 NA
#> 6 Jun-1963 NA
Houses_Under_Construction <- read.csv("/Users/akshayapeduru/Downloads/Houses_Under_Construction.csv", skip = 7)
print(head(Houses_Under_Construction))
#> Period Value
#> 1 Jan-1963 NA
#> 2 Feb-1963 NA
#> 3 Mar-1963 NA
#> 4 Apr-1963 NA
#> 5 May-1963 NA
#> 6 Jun-1963 NA
library(reprex)
library(BigVAR)
#> Loading required package: lattice
#> Warning: package 'lattice' was built under R version 4.2.3
Houses_Completed <- read.csv("/Users/akshayapeduru/Downloads/Houses_Completed.csv", skip = 7)
print(head(Houses_Completed))
#> Period Value
#> 1 Jan-1963 NA
#> 2 Feb-1963 NA
#> 3 Mar-1963 NA
#> 4 Apr-1963 NA
#> 5 May-1963 NA
#> 6 Jun-1963 NA
All_Houses$Value <- as.numeric(as.character(All_Houses$Value))
sum(is.na(All_Houses$Value))
#> [1] 10
Houses_Not_Started$Value <- as.numeric(as.character(Houses_Not_Started$Value))
sum(is.na(Houses_Not_Started$Value))
#> [1] 442
Houses_Under_Construction$Value <- as.numeric(as.character(Houses_Under_Construction$Value))
sum(is.na(Houses_Under_Construction$Value))
#> [1] 442
Houses_Completed$Value <- as.numeric(as.character(Houses_Completed$Value))
sum(is.na(Houses_Completed$Value))
#> [1] 442
All_Houses <- All_Houses[!is.na(All_Houses$Value), ]
TSe_All_Houses <- ts(All_Houses$Value, start=c(1963, 1), frequency=12)
Houses_Not_Started <- Houses_Not_Started[!is.na(Houses_Not_Started$Value), ]
TSe_Houses_Not_Started <- ts(Houses_Not_Started$Value, start=c(1963, 1), frequency=12)
Houses_Under_Construction <- Houses_Under_Construction[!is.na(Houses_Under_Construction$Value), ]
TSe_Houses_Under_Construction <- ts(Houses_Under_Construction$Value, start=c(1963, 1), frequency=12)
Houses_Completed <- Houses_Completed[!is.na(Houses_Completed$Value), ]
TSe_Houses_Completed <- ts(Houses_Completed$Value, start=c(1963, 1), frequency=12)
plot(TSe_All_Houses, main="All Houses", xlab="Year", ylab="Houses Sold")
plot(TSe_Houses_Not_Started, main="Houses Not Started", xlab="Year", ylab="Houses Sold")
plot(TSe_Houses_Under_Construction, main="Houses Under Construction", xlab="Year", ylab="Houses Sold")
plot(TSe_Houses_Completed, main="Houses Completed", xlab="Year", ylab="Houses Sold")
D_All_Houses <- stl(TSe_All_Houses, s.window="periodic")
plot(D_All_Houses)
D_Houses_Not_Started <- stl(TSe_Houses_Not_Started, s.window="periodic")
plot(D_Houses_Not_Started)
D_Houses_Under_Construction <- stl(TSe_Houses_Under_Construction, s.window="periodic")
plot(D_Houses_Under_Construction)
D_Houses_Completed <- stl(TSe_Houses_Completed, s.window="periodic")
plot(D_Houses_Completed)
adf.test(TSe_All_Houses)
#>
#> Augmented Dickey-Fuller Test
#>
#> data: TSe_All_Houses
#> Dickey-Fuller = -2.3546, Lag order = 9, p-value = 0.4282
#> alternative hypothesis: stationary
adf.test(TSe_Houses_Not_Started)
#>
#> Augmented Dickey-Fuller Test
#>
#> data: TSe_Houses_Not_Started
#> Dickey-Fuller = -1.4368, Lag order = 6, p-value = 0.8137
#> alternative hypothesis: stationary
adf.test(TSe_Houses_Under_Construction)
#>
#> Augmented Dickey-Fuller Test
#>
#> data: TSe_Houses_Under_Construction
#> Dickey-Fuller = -1.2637, Lag order = 6, p-value = 0.8867
#> alternative hypothesis: stationary
adf.test(TSe_Houses_Completed)
#>
#> Augmented Dickey-Fuller Test
#>
#> data: TSe_Houses_Completed
#> Dickey-Fuller = -1.4675, Lag order = 6, p-value = 0.8008
#> alternative hypothesis: stationary
F_All_Houses <- auto.arima(TSe_All_Houses)
summary(F_All_Houses)
#> Series: TSe_All_Houses
#> ARIMA(1,1,2)(1,0,2)[12]
#>
#> Coefficients:
#> ar1 ma1 ma2 sar1 sma1 sma2
#> -0.8634 0.6358 -0.2359 0.2948 -0.4085 -0.1094
#> s.e. 0.1052 0.1083 0.0378 0.2197 0.2194 0.0549
#>
#> sigma^2 = 2190: log likelihood = -3856.63
#> AIC=7727.26 AICc=7727.42 BIC=7759.44
#>
#> Training set error measures:
#> ME RMSE MAE MPE MAPE MASE
#> Training set 0.2624641 46.57831 35.8077 -0.408953 5.6687 0.3646529
#> ACF1
#> Training set -0.0001323341
F_Houses_Not_Started <- auto.arima(TSe_Houses_Not_Started)
summary(F_Houses_Not_Started)
#> Series: TSe_Houses_Not_Started
#> ARIMA(0,1,1)
#>
#> Coefficients:
#> ma1
#> -0.2415
#> s.e. 0.0542
#>
#> sigma^2 = 644.2: log likelihood = -1400.07
#> AIC=2804.15 AICc=2804.19 BIC=2811.56
#>
#> Training set error measures:
#> ME RMSE MAE MPE MAPE MASE
#> Training set -1.066121 25.29757 18.18945 -1.515353 9.201286 0.3416855
#> ACF1
#> Training set -0.01204622
F_Houses_Under_Construction <- auto.arima(TSe_Houses_Under_Construction)
summary(F_Houses_Under_Construction)
#> Series: TSe_Houses_Under_Construction
#> ARIMA(0,1,1)
#>
#> Coefficients:
#> ma1
#> -0.3882
#> s.e. 0.0521
#>
#> sigma^2 = 694.5: log likelihood = -1411.44
#> AIC=2826.87 AICc=2826.91 BIC=2834.29
#>
#> Training set error measures:
#> ME RMSE MAE MPE MAPE MASE
#> Training set -0.381581 26.26632 19.26672 -0.9068271 8.024289 0.4114394
#> ACF1
#> Training set -0.007683403
F_Houses_Completed <- auto.arima(TSe_Houses_Completed)
summary(F_Houses_Completed)
#> Series: TSe_Houses_Completed
#> ARIMA(2,1,0)
#>
#> Coefficients:
#> ar1 ar2
#> -0.3933 -0.2526
#> s.e. 0.0558 0.0557
#>
#> sigma^2 = 471.2: log likelihood = -1352.57
#> AIC=2711.15 AICc=2711.23 BIC=2722.27
#>
#> Training set error measures:
#> ME RMSE MAE MPE MAPE MASE
#> Training set 0.5397674 21.59822 16.79712 -0.393783 7.574252 0.4767238
#> ACF1
#> Training set 0.008029448
checkresiduals(F_All_Houses)
#>
#> Ljung-Box test
#>
#> data: Residuals from ARIMA(1,1,2)(1,0,2)[12]
#> Q* = 41.137, df = 18, p-value = 0.001457
#>
#> Model df: 6. Total lags used: 24
checkresiduals(F_Houses_Not_Started)
#>
#> Ljung-Box test
#>
#> data: Residuals from ARIMA(0,1,1)
#> Q* = 54.172, df = 23, p-value = 0.0002536
#>
#> Model df: 1. Total lags used: 24
checkresiduals(F_Houses_Under_Construction)
#>
#> Ljung-Box test
#>
#> data: Residuals from ARIMA(0,1,1)
#> Q* = 46.714, df = 23, p-value = 0.002436
#>
#> Model df: 1. Total lags used: 24
checkresiduals(F_Houses_Completed)
#>
#> Ljung-Box test
#>
#> data: Residuals from ARIMA(2,1,0)
#> Q* = 26.283, df = 22, p-value = 0.2397
#>
#> Model df: 2. Total lags used: 24
acf(TSe_All_Houses, main="ACF for All Houses")
acf(TSe_Houses_Not_Started, main="ACF for Houses not started")
acf(TSe_Houses_Under_Construction, main="ACF for Houses under construction")
acf(TSe_Houses_Completed, main="ACF for completed houses")
pacf(TSe_All_Houses, main="PACF for All Houses")
pacf(TSe_Houses_Not_Started, main="PACF for Houses not started")
pacf(TSe_Houses_Under_Construction, main="PACF for Houses under construction")
pacf(TSe_Houses_Completed, main="PACF for completed houses")
min_length <- min(length(TSe_All_Houses), length(TSe_Houses_Not_Started), length(TSe_Houses_Under_Construction), length(TSe_Houses_Completed))
TSe_All_Houses_t <- TSe_All_Houses[1:min_length]
TSe_Houses_Not_Started_t <- TSe_Houses_Not_Started[1:min_length]
TSe_Houses_Under_Construction_t <- TSe_Houses_Under_Construction[1:min_length]
TSe_Houses_Completed_t <- TSe_Houses_Completed[1:min_length]
data_combined <- data.frame(All_Houses = TSe_All_Houses_t, Houses_Not_Started = TSe_Houses_Not_Started_t, Houses_Under_Construction = TSe_Houses_Under_Construction_t, Houses_Completed = TSe_Houses_Completed_t)
data_TSe<- ts(data_combined, frequency=12, start=c(1963, 1))
var1_m <- VAR(data_TSe, type="both",p=1)
summary(var1_m)
#>
#> VAR Estimation Results:
#> =========================
#> Endogenous variables: All_Houses, Houses_Not_Started, Houses_Under_Construction, Houses_Completed
#> Deterministic variables: both
#> Sample size: 301
#> Log Likelihood: -5742.372
#> Roots of the characteristic polynomial:
#> 0.9791 0.9123 0.8877 0.7336
#> Call:
#> VAR(y = data_TSe, p = 1, type = "both")
#>
#>
#> Estimation results for equation All_Houses:
#> ===========================================
#> All_Houses = All_Houses.l1 + Houses_Not_Started.l1 + Houses_Under_Construction.l1 + Houses_Completed.l1 + const + trend
#>
#> Estimate Std. Error t value Pr(>|t|)
#> All_Houses.l1 0.9115526 0.0241476 37.749 < 2e-16 ***
#> Houses_Not_Started.l1 -0.0837090 0.0567143 -1.476 0.14102
#> Houses_Under_Construction.l1 0.0493632 0.0569198 0.867 0.38652
#> Houses_Completed.l1 0.0155610 0.0542639 0.287 0.77449
#> const 55.3301671 21.0481597 2.629 0.00902 **
#> trend -0.0005751 0.0413458 -0.014 0.98891
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> Residual standard error: 45.01 on 295 degrees of freedom
#> Multiple R-Squared: 0.874, Adjusted R-squared: 0.8719
#> F-statistic: 409.3 on 5 and 295 DF, p-value: < 2.2e-16
#>
#>
#> Estimation results for equation Houses_Not_Started:
#> ===================================================
#> Houses_Not_Started = All_Houses.l1 + Houses_Not_Started.l1 + Houses_Under_Construction.l1 + Houses_Completed.l1 + const + trend
#>
#> Estimate Std. Error t value Pr(>|t|)
#> All_Houses.l1 -0.02414 0.01380 -1.750 0.08123 .
#> Houses_Not_Started.l1 0.87719 0.03240 27.070 < 2e-16 ***
#> Houses_Under_Construction.l1 0.09313 0.03252 2.864 0.00449 **
#> Houses_Completed.l1 -0.01010 0.03100 -0.326 0.74488
#> const 27.59281 12.02633 2.294 0.02247 *
#> trend -0.05753 0.02362 -2.435 0.01548 *
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> Residual standard error: 25.72 on 295 degrees of freedom
#> Multiple R-Squared: 0.9608, Adjusted R-squared: 0.9602
#> F-statistic: 1448 on 5 and 295 DF, p-value: < 2.2e-16
#>
#>
#> Estimation results for equation Houses_Under_Construction:
#> ==========================================================
#> Houses_Under_Construction = All_Houses.l1 + Houses_Not_Started.l1 + Houses_Under_Construction.l1 + Houses_Completed.l1 + const + trend
#>
#> Estimate Std. Error t value Pr(>|t|)
#> All_Houses.l1 -0.001029 0.014766 -0.070 0.9445
#> Houses_Not_Started.l1 0.138674 0.034680 3.999 8.06e-05 ***
#> Houses_Under_Construction.l1 0.842588 0.034806 24.208 < 2e-16 ***
#> Houses_Completed.l1 0.008288 0.033182 0.250 0.8029
#> const -0.911943 12.870754 -0.071 0.9436
#> trend 0.063410 0.025283 2.508 0.0127 *
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> Residual standard error: 27.52 on 295 degrees of freedom
#> Multiple R-Squared: 0.942, Adjusted R-squared: 0.941
#> F-statistic: 958.4 on 5 and 295 DF, p-value: < 2.2e-16
#>
#>
#> Estimation results for equation Houses_Completed:
#> =================================================
#> Houses_Completed = All_Houses.l1 + Houses_Not_Started.l1 + Houses_Under_Construction.l1 + Houses_Completed.l1 + const + trend
#>
#> Estimate Std. Error t value Pr(>|t|)
#> All_Houses.l1 -0.0131837 0.0123836 -1.065 0.2879
#> Houses_Not_Started.l1 0.0007554 0.0290849 0.026 0.9793
#> Houses_Under_Construction.l1 0.0363783 0.0291903 1.246 0.2137
#> Houses_Completed.l1 0.8813374 0.0278282 31.671 <2e-16 ***
#> const 24.2426945 10.7941494 2.246 0.0254 *
#> trend 0.0057398 0.0212034 0.271 0.7868
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> Residual standard error: 23.08 on 295 degrees of freedom
#> Multiple R-Squared: 0.8697, Adjusted R-squared: 0.8674
#> F-statistic: 393.6 on 5 and 295 DF, p-value: < 2.2e-16
#>
#>
#>
#> Covariance matrix of residuals:
#> All_Houses Houses_Not_Started
#> All_Houses 2025.808 17.78
#> Houses_Not_Started 17.784 661.36
#> Houses_Under_Construction 5.268 161.90
#> Houses_Completed -57.793 46.92
#> Houses_Under_Construction Houses_Completed
#> All_Houses 5.268 -57.79
#> Houses_Not_Started 161.903 46.92
#> Houses_Under_Construction 757.492 169.62
#> Houses_Completed 169.615 532.78
#>
#> Correlation matrix of residuals:
#> All_Houses Houses_Not_Started
#> All_Houses 1.000000 0.01536
#> Houses_Not_Started 0.015364 1.00000
#> Houses_Under_Construction 0.004253 0.22874
#> Houses_Completed -0.055629 0.07904
#> Houses_Under_Construction Houses_Completed
#> All_Houses 0.004253 -0.05563
#> Houses_Not_Started 0.228744 0.07904
#> Houses_Under_Construction 1.000000 0.26699
#> Houses_Completed 0.266995 1.00000
lag_select <- VARselect(data_TSe, type="both", lag.max=10,)
opt_lags <- lag_select$selection["AIC(n)"]
varp_m <- VAR(data_TSe, type="both", p=opt_lags,)
summary(varp_m)
#>
#> VAR Estimation Results:
#> =========================
#> Endogenous variables: All_Houses, Houses_Not_Started, Houses_Under_Construction, Houses_Completed
#> Deterministic variables: both
#> Sample size: 299
#> Log Likelihood: -5629.097
#> Roots of the characteristic polynomial:
#> 0.9758 0.9758 0.9442 0.8969 0.5263 0.5263 0.5003 0.5003 0.3725 0.1773 0.1521 0.1521
#> Call:
#> VAR(y = data_TSe, p = opt_lags, type = "both")
#>
#>
#> Estimation results for equation All_Houses:
#> ===========================================
#> All_Houses = All_Houses.l1 + Houses_Not_Started.l1 + Houses_Under_Construction.l1 + Houses_Completed.l1 + All_Houses.l2 + Houses_Not_Started.l2 + Houses_Under_Construction.l2 + Houses_Completed.l2 + All_Houses.l3 + Houses_Not_Started.l3 + Houses_Under_Construction.l3 + Houses_Completed.l3 + const + trend
#>
#> Estimate Std. Error t value Pr(>|t|)
#> All_Houses.l1 0.806326 0.059237 13.612 <2e-16 ***
#> Houses_Not_Started.l1 -0.099270 0.110186 -0.901 0.3684
#> Houses_Under_Construction.l1 0.065466 0.107138 0.611 0.5417
#> Houses_Completed.l1 0.103924 0.122296 0.850 0.3962
#> All_Houses.l2 0.092182 0.075462 1.222 0.2229
#> Houses_Not_Started.l2 0.002864 0.129002 0.022 0.9823
#> Houses_Under_Construction.l2 0.062661 0.117313 0.534 0.5937
#> Houses_Completed.l2 -0.247902 0.141376 -1.753 0.0806 .
#> All_Houses.l3 0.028256 0.058553 0.483 0.6298
#> Houses_Not_Started.l3 0.025111 0.109009 0.230 0.8180
#> Houses_Under_Construction.l3 -0.080000 0.105734 -0.757 0.4499
#> Houses_Completed.l3 0.147971 0.123062 1.202 0.2302
#> const 48.505142 21.995375 2.205 0.0282 *
#> trend -0.010926 0.042841 -0.255 0.7989
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> Residual standard error: 44.56 on 285 degrees of freedom
#> Multiple R-Squared: 0.8798, Adjusted R-squared: 0.8743
#> F-statistic: 160.4 on 13 and 285 DF, p-value: < 2.2e-16
#>
#>
#> Estimation results for equation Houses_Not_Started:
#> ===================================================
#> Houses_Not_Started = All_Houses.l1 + Houses_Not_Started.l1 + Houses_Under_Construction.l1 + Houses_Completed.l1 + All_Houses.l2 + Houses_Not_Started.l2 + Houses_Under_Construction.l2 + Houses_Completed.l2 + All_Houses.l3 + Houses_Not_Started.l3 + Houses_Under_Construction.l3 + Houses_Completed.l3 + const + trend
#>
#> Estimate Std. Error t value Pr(>|t|)
#> All_Houses.l1 -0.036667 0.032865 -1.116 0.26550
#> Houses_Not_Started.l1 0.661609 0.061132 10.823 < 2e-16 ***
#> Houses_Under_Construction.l1 0.191177 0.059441 3.216 0.00145 **
#> Houses_Completed.l1 0.167271 0.067851 2.465 0.01428 *
#> All_Houses.l2 0.003475 0.041867 0.083 0.93391
#> Houses_Not_Started.l2 0.287112 0.071571 4.012 7.71e-05 ***
#> Houses_Under_Construction.l2 -0.060719 0.065086 -0.933 0.35166
#> Houses_Completed.l2 -0.176780 0.078436 -2.254 0.02497 *
#> All_Houses.l3 0.019651 0.032486 0.605 0.54573
#> Houses_Not_Started.l3 -0.009821 0.060479 -0.162 0.87112
#> Houses_Under_Construction.l3 -0.091566 0.058662 -1.561 0.11965
#> Houses_Completed.l3 -0.012069 0.068276 -0.177 0.85981
#> const 21.452016 12.203199 1.758 0.07984 .
#> trend -0.039610 0.023768 -1.666 0.09672 .
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> Residual standard error: 24.72 on 285 degrees of freedom
#> Multiple R-Squared: 0.9649, Adjusted R-squared: 0.9633
#> F-statistic: 603.2 on 13 and 285 DF, p-value: < 2.2e-16
#>
#>
#> Estimation results for equation Houses_Under_Construction:
#> ==========================================================
#> Houses_Under_Construction = All_Houses.l1 + Houses_Not_Started.l1 + Houses_Under_Construction.l1 + Houses_Completed.l1 + All_Houses.l2 + Houses_Not_Started.l2 + Houses_Under_Construction.l2 + Houses_Completed.l2 + All_Houses.l3 + Houses_Not_Started.l3 + Houses_Under_Construction.l3 + Houses_Completed.l3 + const + trend
#>
#> Estimate Std. Error t value Pr(>|t|)
#> All_Houses.l1 -0.002853 0.034395 -0.083 0.93396
#> Houses_Not_Started.l1 0.029299 0.063978 0.458 0.64733
#> Houses_Under_Construction.l1 0.550766 0.062208 8.854 < 2e-16 ***
#> Houses_Completed.l1 0.059138 0.071010 0.833 0.40565
#> All_Houses.l2 -0.032793 0.043816 -0.748 0.45482
#> Houses_Not_Started.l2 0.188880 0.074903 2.522 0.01223 *
#> Houses_Under_Construction.l2 0.193233 0.068116 2.837 0.00488 **
#> Houses_Completed.l2 0.048423 0.082088 0.590 0.55573
#> All_Houses.l3 0.032421 0.033998 0.954 0.34109
#> Houses_Not_Started.l3 -0.113352 0.063294 -1.791 0.07438 .
#> Houses_Under_Construction.l3 0.151107 0.061393 2.461 0.01444 *
#> Houses_Completed.l3 -0.128855 0.071454 -1.803 0.07239 .
#> const 1.866551 12.771288 0.146 0.88390
#> trend 0.055907 0.024875 2.248 0.02537 *
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> Residual standard error: 25.87 on 285 degrees of freedom
#> Multiple R-Squared: 0.9503, Adjusted R-squared: 0.9481
#> F-statistic: 419.4 on 13 and 285 DF, p-value: < 2.2e-16
#>
#>
#> Estimation results for equation Houses_Completed:
#> =================================================
#> Houses_Completed = All_Houses.l1 + Houses_Not_Started.l1 + Houses_Under_Construction.l1 + Houses_Completed.l1 + All_Houses.l2 + Houses_Not_Started.l2 + Houses_Under_Construction.l2 + Houses_Completed.l2 + All_Houses.l3 + Houses_Not_Started.l3 + Houses_Under_Construction.l3 + Houses_Completed.l3 + const + trend
#>
#> Estimate Std. Error t value Pr(>|t|)
#> All_Houses.l1 0.003486 0.028635 0.122 0.90320
#> Houses_Not_Started.l1 -0.003717 0.053264 -0.070 0.94441
#> Houses_Under_Construction.l1 -0.007191 0.051790 -0.139 0.88966
#> Houses_Completed.l1 0.584435 0.059118 9.886 < 2e-16 ***
#> All_Houses.l2 -0.064935 0.036478 -1.780 0.07613 .
#> Houses_Not_Started.l2 0.076236 0.062360 1.223 0.22252
#> Houses_Under_Construction.l2 -0.032391 0.056709 -0.571 0.56833
#> Houses_Completed.l2 0.116283 0.068341 1.702 0.08994 .
#> All_Houses.l3 0.047710 0.028305 1.686 0.09297 .
#> Houses_Not_Started.l3 -0.091497 0.052695 -1.736 0.08358 .
#> Houses_Under_Construction.l3 0.087647 0.051112 1.715 0.08747 .
#> Houses_Completed.l3 0.221952 0.059488 3.731 0.00023 ***
#> const 17.129689 10.632561 1.611 0.10827
#> trend 0.003784 0.020709 0.183 0.85517
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#>
#> Residual standard error: 21.54 on 285 degrees of freedom
#> Multiple R-Squared: 0.8903, Adjusted R-squared: 0.8853
#> F-statistic: 177.9 on 13 and 285 DF, p-value: < 2.2e-16
#>
#>
#>
#> Covariance matrix of residuals:
#> All_Houses Houses_Not_Started
#> All_Houses 1985.330 -18.20
#> Houses_Not_Started -18.197 611.11
#> Houses_Under_Construction 9.165 175.04
#> Houses_Completed -38.974 75.56
#> Houses_Under_Construction Houses_Completed
#> All_Houses 9.165 -38.97
#> Houses_Not_Started 175.038 75.56
#> Houses_Under_Construction 669.329 150.88
#> Houses_Completed 150.877 463.92
#>
#> Correlation matrix of residuals:
#> All_Houses Houses_Not_Started
#> All_Houses 1.000000 -0.01652
#> Houses_Not_Started -0.016521 1.00000
#> Houses_Under_Construction 0.007951 0.27369
#> Houses_Completed -0.040610 0.14191
#> Houses_Under_Construction Houses_Completed
#> All_Houses 0.007951 -0.04061
#> Houses_Not_Started 0.273686 0.14191
#> Houses_Under_Construction 1.000000 0.27076
#> Houses_Completed 0.270757 1.00000
Var1_AIC <- AIC(var1_m)
Var1_BIC <- BIC(var1_m)
Varp_AIC <- AIC(varp_m)
Varp_BIC <- BIC(varp_m)
cat("VAR(1) AIC", Var1_AIC, "\n BIC", Var1_BIC, "\n")
#> VAR(1) AIC 11532.74
#> BIC 11621.71
cat("VAR(p) AIC", Varp_AIC, "\n BIC", Varp_BIC, "\n")
#> VAR(p) AIC 11370.19
#> BIC 11577.42
if(Var1_AIC < Varp_AIC && Var1_BIC < Varp_BIC) {
cat("Based on the AIC and BIC criteria, the VAR(1) model is the preferred choice.\n")
} else if(Varp_AIC < Var1_AIC && Varp_BIC < Var1_BIC) {
cat("Based on the AIC and BIC criteria, the VAR(p) model is the preferred choice..\n")
} else {
cat("Additional diagnostics and factors may need to be evaluated.\n")
}
#> Based on the AIC and BIC criteria, the VAR(p) model is the preferred choice..
f_var1 <- predict(var1_m, n.ahead=1)
f_varp <- predict(varp_m, n.ahead=1)
print(f_var1)
#> $All_Houses
#> fcst lower upper CI
#> All_Houses.fcst 671.9503 583.7343 760.1663 88.21597
#>
#> $Houses_Not_Started
#> fcst lower upper CI
#> Houses_Not_Started.fcst 90.41392 40.00979 140.8181 50.40414
#>
#> $Houses_Under_Construction
#> fcst lower upper CI
#> Houses_Under_Construction.fcst 284.7912 230.848 338.7345 53.94325
#>
#> $Houses_Completed
#> fcst lower upper CI
#> Houses_Completed.fcst 275.0266 229.7867 320.2665 45.23989
print(f_varp)
#> $All_Houses
#> fcst lower upper CI
#> All_Houses.fcst 659.1575 571.8273 746.4877 87.3302
#>
#> $Houses_Not_Started
#> fcst lower upper CI
#> Houses_Not_Started.fcst 87.51118 39.05973 135.9626 48.45145
#>
#> $Houses_Under_Construction
#> fcst lower upper CI
#> Houses_Under_Construction.fcst 280.5758 229.8688 331.2828 50.70699
#>
#> $Houses_Completed
#> fcst lower upper CI
#> Houses_Completed.fcst 282.5343 240.3189 324.7497 42.21541
plot(f_var1, main="One-Month Forecast Based on a First-Order Vector Autoregression (VAR(1)) Model")
plot(f_varp, main="One-Month Forecast Based on VAR(p) Model")
test_gag <- causality(varp_m)
#> Warning in causality(varp_m):
#> Argument 'cause' has not been specified;
#> using first variable in 'x$y' (All_Houses) as cause variable.
print(test_gag)
#> $Granger
#>
#> Granger causality H0: All_Houses do not Granger-cause
#> Houses_Not_Started Houses_Under_Construction Houses_Completed
#>
#> data: VAR object varp_m
#> F-Test = 0.83935, df1 = 9, df2 = 1140, p-value = 0.5798
#>
#>
#> $Instant
#>
#> H0: No instantaneous causality between: All_Houses and
#> Houses_Not_Started Houses_Under_Construction Houses_Completed
#>
#> data: VAR object varp_m
#> Chi-squared = 0.68609, df = 3, p-value = 0.8765
data_m <- as.matrix(data_TSe)
s_var_m <- BigVAR.fit(data_m,lambda = 0.1,p = 16, struct = "Lag")
print(summary(s_var_m))
#> Min. 1st Qu. Median Mean 3rd Qu. Max.
#> -5.85423 -0.05124 0.00143 0.41160 0.07419 68.16797Created on 2024-04-11 with reprex v2.0.2
HW_1_ICNSA.pdf So I forecast the new data release value will be 339658.3 with confidence interval (102326.4, 576990.2)