Introduction

Point forecasting is a critical aspect of time series analysis, enabling us to predict future values based on historical data. When dealing with time series that exhibit seasonality, the construction of h-step-ahead point forecasts becomes more intricate due to the repeating patterns observed over specific periods. In this chapter, we will delve into the methodology of creating forecasts for multiple steps ahead while accounting for seasonality effects. We will explore techniques to ensure accurate predictions that capture the inherent cyclical behavior of the time series.

h-Step-Ahead Point Forecasting with Seasonality

When constructing h-step-ahead point forecasts for a time series with seasonality, we consider how the seasonal patterns impact future values. The term “h” represents the number of periods into the future we aim to forecast. Seasonality introduces periodic fluctuations in the data, and accurate forecasting requires accounting for these cycles.

Forecasting Techniques for Seasonal Time Series

To construct an h-step-ahead point forecast, we need to account for both the trend and the seasonal component of the time series. The techniques employed can vary based on the complexity of the seasonality. For instance, when dealing with additive seasonality, we add the seasonal factor to the trend component. Conversely, in the case of multiplicative seasonality, we multiply the trend component by the seasonal factor.

• h-Step-Ahead Point Forecast with Additive Seasonality: For a time series with additive seasonality, the h-step-ahead point forecast can be calculated using the formula:

$$\text{Forecast}_{t+h}= \text{Trend}_t + \text{Seasonal Factor}_{t+h}$$

• h-Step-Ahead Point Forecast with Multiplicative Seasonality: For a time series with multiplicative seasonality, the $h$-step-ahead point forecast is calculated as:

$$\text{Forecast}_{t+h} = \text{Trend}_t \times \text{Seasonal Factor}_{t+h}$$