ARIMA Forecasting Techniques

Autoregressive models (AR models) assume that the residuals of the model are white noise.

ARIMA models can be extended to include seasonal components in SARIMA models.

The forecasting step in time series analysis involves generating predictions based on the known model parameters.

Model diagnostics for ARIMA models involve examining residuals for autocorrelation and normality.

Recursive forecasting in time series analysis involves generating forecasts for a specific future period beyond the available data.

The ACF plot is used to examine autocorrelation in time series data.

The Autocorrelation Function (ACF) measures the correlation between a time series and its leading values.

Partial Autocorrelation Function (PACF) is a tool used in time series analysis to understand the correlation structure of a time series.

The ACF helps identify the presence of autocorrelation, which is the correlation between observations at the same time point.

In ACF(h) = Correlation(Y(t), Y(t-h)), 'Y(t)' represents the time series at time t.

PACF is usually plotted as a function of the lead, with the correlation coefficient on the y-axis and the lead on the x-axis.

Autoregressive models like ARIMA are commonly used for forecasting in time series analysis.

Significant positive values at lag h in the PACF plot indicate a direct relationship between observations at lag h.

Non-significant PACF values at higher lags suggest that the relationship between observations t and t-h is primarily explained by intermediate lags.

ACF and PACF plots are useful in determining appropriate lag orders for Moving Average (MA) models only.

ARIMA models involve identification, estimation, and forecasting steps.

The first step in building an ARIMA model is to identify the appropriate order of integration (d), autoregressive (p), and moving average (q) components.

To check if a time series is stationary, one should analyze the mean, variance, and autocovariance over time.