Basic Forecasting

Abstract

A time series is a set of numerical data collected at regular intervals over time, to be denoted $Y_{t} \left( {t = 1, \ldots , T} \right)$ hereafter. The data may be collected annually, semi-annually or monthly. The goal of time series analysis is to use historical data patterns to create a model which can then be used for forecasting. The analysis usually consists of three components: descriptive analysis, modelling and forecasting. In the descriptive analysis stage, the data is observed over time to find a long-term trend. In the modelling stage, a model is fitted to the data based on the properties in the data. For forecasting, the model derived in the modelling stage is used to predict future values. In this chapter, we will discuss the descriptive analysis stage and focus on the moving average smoothing and exponential smoothing methods to identify the long-term trend. We will then discuss the modelling and forecasting stages in Chap. 4.