R Language Decomposition And Forecasting Intro Complete Guide

R Language Decomposition and Forecasting Introduction

Time Series Decomposition

Time Series Decomposition is a method used to break down a time series into several distinct components in order to make the underlying data more interpretable. Typically, a time series is decomposed into three main components:

1. Trend: This represents the long-term pattern or direction in which the variable is moving. For example, if a dataset shows increasing sales over the years, then there's an upward trend.

2. Seasonality: It indicates regular patterns that repeat at specific intervals within the time series. Monthly sales data that consistently peak around Black Friday would exhibit strong seasonality.

3. Random (Irregular/Residual) Variance: This captures the random fluctuations in the data that do not follow any predictable pattern.

In R, one of the most widely used functions for decomposing time series data is decompose(), which operates on an object of class "ts" (time series). This function assumes that the time series is additive in nature, meaning it can be represented as the sum of the trend, seasonal, and random components.

Steps to Perform Time Series Decomposition:

• Convert your data into a time series object using the ts() function.
• Apply the decompose() function to the time series object.
• Plot the results using plot() function to visualize individual components.

# Sample data creation
data <- c(112, 118, 132, 129, 121, 135, 148, 148, 136, 119, 104, 118, 115, 126, 141, 
          135, 125, 149, 170, 170, 158, 133, 114, 140)
sales_ts <- ts(data, start=c(1949, 1), frequency=12)

# Decompose the time series
decomposed_sales <- decompose(sales_ts)

# Plot the decomposition
plot(decomposed_sales)

Output Explanation: The plot() function applied to the decomposed object shows four panels:

• Original Time Series
• Estimated Trend Component
• Seasonal Component
• Random/Residual Component

Forecasting in R

Forecasting involves predicting future values based on historical data. In R, several packages support forecasting, including forecast, fpp2, tseries, and stats.

Basic Steps to Perform Forecasting:

• Load necessary packages.
• Convert data into a time series object.
• Choose an appropriate forecasting model such as AutoRegressive Integrated Moving Average (ARIMA), Exponential Smoothing State Space Model (ETS), or others.
• Fit the model to the data.
• Generate forecasts and confidence intervals.
• Plot forecasts along with original observations.

ARIMA Models: ARIMA models are used for forecasting where the data exhibit a strong autocorrelation. These models are denoted by three parameters: AR(p), I(d), MA(q):

• p: Lag order (the number of lagged values used).
• d: Degree of differencing.
• q: Moving average window size.

Steps with ARIMA in R:

• Install and load the forecast package.
• Fit ARIMA model using auto.arima() function for automatic parameter selection.
• Forecast future values using forecast() function.
• Plot results with autoplot().

# Install and load forecast package
install.packages("forecast")
library(forecast)

# Load time series data into ts()
sales_ts <- ts(AirPassengers, start=c(1949, 1), frequency=12)

# Fit ARIMA model
fit <- auto.arima(sales_ts)

# Forecast next 10 periods
forecasts <- forecast(fit, h = 10)

# Plot forecasts and actual series
autoplot(forecasts)

ETS Models: ETS models are useful for datasets with both trend and seasonality. They consist of three components: Error, Trend, and Seasonality and can be either additive or multiplicative.

Steps with ETS in R:

• Use ets() function from forecast package.
• Generate forecasts with forecast() function.
• Plot the forecasts using autoplot().

# Fit ETS model
fit_ets <- ets(sales_ts)

# Forecast next 10 periods
forecasts_ets <- forecast(fit_ets, h = 10)

# Plot forecasts and actual series
autoplot(forecasts_ets)

Important Considerations:

• Stationarity: Many forecasting models assume that the data is stationary, i.e., it has constant mean, variance, and autocovariance. Non-stationary data may require transformation like differencing.
• Model Diagnostics: Post fitting, diagnostics checks like ACF/PACF plots, residuals analysis should be performed to validate that the chosen model fits well and is reliable for forecasting.
• Choosing Between ARIMA and ETS: The choice often depends on the nature of your data (additive vs. multiplicative seasonality) and whether it follows a moving average structure.
• Accuracy Measurement: Different measures like Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and others help in assessing the accuracy of forecasts. Always compare multiple models based on these metrics before finalizing a forecast method.