70. TIME SERIES ANALYSIS

OBJECTIVE

Forecast the demand for the next periods.

DESCRIPTION

Time series analysis is useful for forecasting based on the patterns underlying the past data. There are four main components:

• - Trend: a long-term movement concerning time series that can be upward, downward, or stationary (an example can be the upward trend in population growth);
• -  Cyclical: a pattern that is usually observed over two or more years, and it is caused by circumstances that repeat in cycles (for example economic cycles, which present four phases: prosperity, decline, depression, and recovery);
• -     Seasonal: variations within a year that usually depend on the weather, customers’ habits, and so on;
• - Irregular components: random events with unpredictable influences on the time series.

Time Series Analysis

There are two main types of models depending on how the previous four components are included:

(     1)    Y(t)=T(t) x S(t) x C(t) x I(t)

Multiplicative models: the four components are multiplied, and in this case we assume that the components can affect each other.

(     2)    Y(t)=T(t) + S(t) + C(t) + I(t)

Additive models: we make the assumption that the components are independent.

Another important element of time series is stationarity. A process is stationary when an event is influenced by a previous event or events. For example, if today the temperature is quite high, it is more likely that tomorrow it will be quite high as well.

There are many models for time series analysis, but one of the most used is ARIMA (autoregressive integrated moving average). There are some variations of it as well as non-linear models. However, linear models such as ARIMA are widely used due to their simplicity of implementation and understanding.

A good time series analysis implies several exploratory analyses and model validation, which requires statistical knowledge and experience. The template contains a simplification of a time series model in which seasonality and trends are isolated to forecast future sales.

The data can be collected at every instance of time (continuous time series), for example temperature reading, or at discrete points of time (discrete time series), when they are observed daily, weekly, monthly, and so on.

TEMPLATE

Download the Time Series Analysis Template