Time Series Analysis and Forecasting By Sahar Zia

Time graph/ Time Plot • displays values against time • Similar to x-y graphs, but while an x-y graph can plot a variety of “x” variables (for example, height, weight, age), • Time plots can only display time on the xaxis.

Time Series Analysis • A time-series is a set of observations on a quantitative variable collected over time. • Examples – Temperature and rainfall Averages – Historical data on tourism activity, growth rate etc • In time series analysis, we analyze the past behavior of a variable in order to predict its future behavior.

Components of time series • Secular/ General Trends: continues to persist (long term 12+ periods) • Seasonal Movements: biannually, quarterly or monthly (short term periods of 1 -2) • Cyclical Movements: Long term oscillation (medium periods of 5 -10 periods) • Irregular Fluctuations- sudden changes which are unlikely to occur again

Components of TSA (Cont. ) • Difficult to forecast demand because. . . – There are no causal variables – The components (trend, seasonality, cycles, and random variation) cannot always be easily or accurately identified

Goals of Time Series Analysis • Time Frame (How far can we predict? ) – short-term (1 - 2 periods) – medium-term (5 - 10 periods) – long-term (12+ periods) – No line of demarcation • Nature of phenomena/trend • Future Prediction

Secular trends • • Freehand curve Semi-averages Moving averages Least square

Semi-averages

Moving Averages

Least Square

Least square

Analyzing seasonal variations • • Percent of annual average method Ratio-to moving average method The ratio to trend method Link-relative method

Percent of annual average method

The ratio-to-Trend method

Analyzing cyclic/irregular variations • Residual method • Harmonic analysis