SARIMA MLM

Question 1

Seasonal Autoregressive Integrated Moving-Average (SARIMA)

Answer 1

Seasonal Autoregressive Integrated Moving-Average (SARIMA) models are a generalization of ARIMA models to handle seasonal data.

Question 2

1. Introduction

Answer 2

SARIMA stands for Seasonal Autoregressive Integrated Moving Average. These models are used for time series data that exhibits seasonal effects. They are an extension of ARIMA models.

Question 3

2. Autoregressive Component (AR)

Answer 3

The autoregressive part (AR) of SARIMA refers to the use of past values in the regression equation for the series Y. The term ‘p’ is used to denote the order of the autoregressive part of the model.

Question 4

3. Integrated Component (I)

Answer 4

The integrated part (I) in SARIMA represents the differencing of actual observations to make the time series stationary. ‘d’ is the order of differencing in the model.

Question 5

4. Moving Average Component (MA)

Answer 5

The moving average part (MA) in SARIMA represents a dependency between an observation and a residual error from a moving average model. ‘q’ is the order of the moving average part of the model.

Question 6

5. Seasonal Components

Answer 6

In addition to the non-seasonal AR, I, and MA terms, SARIMA models have additional seasonal components: SAR, SI, and SMA represented as ‘P’, ‘D’, ‘Q’, and an additional parameter ‘s’ for the periodicity of the time series (i.e., the number of periods in a season).

Question 7

6. Parameter Estimation

Answer 7

Parameters of the SARIMA model are estimated using methods such as Maximum Likelihood Estimation. The Box-Jenkins methodology can also be applied here, which involves model selection through the autocorrelation and partial autocorrelation plots.

Question 8

7. Forecasting

Answer 8

After the model has been fitted, it can be used for forecasting future points in the time series. Confidence intervals are often provided with these forecasts to indicate the uncertainty in the predictions.

Question 9

8. Strengths and Limitations

Answer 9

SARIMA models are widely used because of their ability to model a variety of time series data with a seasonal component. However, they can be sensitive to the correct specification of the seasonal order ‘s’ and other parameters. Also, SARIMA models assume linear relationships and may struggle with non-linear data.

Question 10

9. SARIMA in Practice

Answer 10

SARIMA models are used in a variety of fields, including economics, finance, environmental science, and engineering. They are especially useful for forecasting metrics that have a clear pattern of seasonality, like electricity demand, tourism arrivals, etc.