[Theory]

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• [ ] ARIMA

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ARIMA Model Overview

AutoRegression Integrated Moving Average (ARIMA) Model

ARIMA is a statistical model used primarily for analyzing and forecasting time series data. Here are some key points about ARIMA:

• AutoRegression: ARIMA uses the dependent relationship between an observation and some number of lagged observations (i.e., previous values).
• Integrated: This involves differencing the observations to make the time series stationary (i.e., the mean and variance do not change over time).
• Moving Average: ARIMA uses the dependency between an observation and a residual error from a moving average model applied to lagged observations.

Key Characteristics of ARIMA:

• Major Usage: It works majorly for time series data.

  • Example: Predicting daily stock prices based on past values.

• Versatility: ARIMA is not limited to time series analysis. It can perform multiple tasks such as:

  • Forecasting weather conditions.
  • Predicting sales based on historical data.

• Data Requirement: It requires historical data to generate predictions.

  • Example: Predicting weather patterns using past weather data.

• Types of Data: ARIMA can handle various types of data, including text, audio, and time series.

  • Example: Using last year's data from Flipkart to predict traffic during different times of the day, which helps in optimizing product deployment (e.g., Terraform, Kubernetes).

Key Concepts

Autoregression (AR):

• An autoregressive model predicts future behavior based on past behavior. It assumes that past values have a linear influence on current values.
• Example: If the traffic on Flipkart was high last year during the Diwali season, an autoregressive model would predict similar high traffic this year, adjusting for other variables.

Conditional Probability:

• This concept is used to predict the likelihood of an event occurring based on the occurrence of a previous event.
• Logistic Regression Formula: ( y = mx + c )
  • Example: If you purchase a phone, you might get a discount on accessories. Such offers are designed based on conditional probability to influence purchase behavior.

Sequential Dependency:

• Sequential dependency refers to the dependence of a current observation on the sequence of past observations.
• This is a crucial concept in time series analysis, as it helps in understanding how past values influence future values.
• Explanation to be added: Sequential dependency is critical in processes where the order of events significantly impacts outcomes, such as in customer purchase behaviors or inventory management.

Example:

• Business Application: Using last year's data from Flipkart to predict website traffic during morning and evening hours. Based on these predictions, the deployment of products related to DevOps (e.g., Terraform, Kubernetes) can be optimized to ensure better performance and availability.

Further Elaboration

Autoregression:

• Autoregression models assume that past values can explain current values. This helps in making future predictions more accurate.
• To be filled with detailed mathematical explanation and real-world application examples.

Sequential Dependency:

• Sequential dependency highlights the importance of the sequence in which data points appear.
• To be filled with an explanation and examples demonstrating the impact of order in various processes.

This overview provides a structured explanation of the ARIMA model, its applications, and key concepts for a better understanding of its functionality and usage.

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Examples of Autoregression Models

1. Stock Market Prediction: Predicting future stock prices based on past closing prices.
2. Weather Forecasting: Forecasting future weather conditions using past weather data.
3. Sales Forecasting: Estimating future sales from historical sales data.
4. Economic Indicators: Predicting economic indicators like GDP growth using past values.
5. Website Traffic Analysis: Forecasting website visitor numbers based on past traffic data.
6. Electricity Load Forecasting: Predicting future electricity demand using historical usage patterns.
7. Natural Resource Management: Estimating future resource consumption from past usage data.
8. Inventory Management: Forecasting inventory needs based on historical sales and stock data.

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Stock market prediction, weather forecasting, sales forecasting, electricity load forecasting, and website traffic analysis are well-suited for ARIMA models.

Why the Other 3 Are Not a Good Choice for ARIMA

1. Economic Indicators: These often involve complex interactions and external factors that ARIMA might not capture effectively.
2. Natural Resource Management: Resource usage can be influenced by many non-time series factors like policy changes and environmental conditions.
3. Inventory Management: This involves discrete events and irregular patterns that may not fit well with ARIMA's assumptions about continuity and stationarity.