Statistics and Modelling 3.1 Credits: 3 Internally Assessed

What is time series data? General Introduction In the following topics, we will review techniques that are useful for analyzing time series data, that is, sequences of measurements that follow non-random orders. Unlike the analyses of random samples of observations that are discussed in the context of most other statistics, the analysis of time series is based on the assumption that successive values in the data file represent consecutive measurements taken at equally spaced time intervals.

In general there are four types of components in Time series analysis: Seasonality, Trend, Cycling, Irregularity.

Trend: A time series may be stationary or exhibit trend over time. Long-term trend is typically modelled as a linear, (quadratic or exponential function).

Trend estimates reveal the smooth, relatively slowly changing features in a time series. They are usually estimated by applying repeated moving averages.

Seasonal variation: When a repetitive pattern is observed over some time horizon, the series is said to have seasonal behaviour. Seasonal effects are usually associated with calendar or climatic changes. Seasonal variation is frequently tied to yearly cycles.

What is the irregular component? This is the part of the observed value that is not included in the trend cycle or the seasonal effects (or in estimated trading day or holiday effects). Its values are unpredictable as regards timing, impact, and duration.

Cyclical variation: An upturn or downturn not tied to seasonal variation. Usually results from changes in economic conditions.