# Associative and Time Series Forecasting Models

Associative and Time Series Forecasting involves using past data to generate a number, set of numbers, or scenario that corresponds to a future occurrence. It is absolutely essential to short-range and long-range planning. Time Series and Associative models are both quantitative forecast techniques are more objective than qualitative techniques such as the Delphi Technique and market research. Time Series Models Based on the assumption that history will repeat itself, there will be identifiable patterns of behaviour that can be used to predict future behaviour.

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This model is useful when you have a short time requirement (eg days) to analyse products in their growth stages to predict short-term outcomes. To use this model you look at several historical periods and choose a method that minimises a chosen measure of error. Then use that method to predict the future. To do this you use detailed data by SKU’s (Stock Keeping Units) which are readily available. In TSM there may be identifiable underlying behaviours to identify as well as the causes of that behaviour.

The data may show causal patterns that appear to repeat themselves – the trick is to determine which are true patterns that can be used for analysis and which are merely random variations. The patterns you look for include: Trends – long term movements in either direction Cycles – wavelike variations lasting more than a year usually tied to economic or political conditions (eg gas prices have long term impact on travel trends) Seasonality – short-term variations related to season, month, particular day (eg Christmas sales, Monday trade etc)

In addition there are causes of behaviour that are not patterns such as worker strikes, natural disasters and other random variations. Simple uses of this model include “naive” forecasting & averaging but both take little account of the variations and patterns. “Naive” forecast uses the actual demand for the past period as the forecasted demand for the next period on the assumption that the past will repeat and any trends, seasonality, or cycles are either reflected in the previous period’s demand or do not exist.

Simple average – takes the average of some number of periods of past data by summing each period and dividing the result by the number of periods. (great for short term basic forecasting) Moving average takes a predetermined number of periods, sums their actual demand, and divides by the number of periods to reach a forecast. For each subsequent period, the oldest period of data drops off and the latest period is added Weighted average applies a predetermined weight to each month of past data, sums the past data from each period then divides by the total of the weights.

If the forecaster adjusts the weights so that their sum is equal to 1, then the weights are multiplied by the actual demand of each applicable period. The results are then summed to achieve a weighted forecast. Generally, the more recent the data is, the higher the weight. Weighted moving average this is a combination of weighted and moving average which assigns weights to a predetermined number of periods of actual data and computes the forecast the same way as moving average forecasts. As with all moving forecasts, as each new period is added, the data from the oldest period is discarded.

Exponential smoothing is a more complex form of weighted moving average in which the weight falls off exponentially as the data ages. This averaging technique takes the previous period’s forecast and adjusts it by a predetermined smoothing constant multiplied by the difference in the previous forecast and the demand that actually occurred during the previously forecasted period (called forecast error). Holt’s Model An extension of exponential smoothing used when time-series data exhibits a linear trend.

This method is known by several other names: double smoothing; trend-adjusted exponential smoothing; forecast including trend. A more complex form known as the Holt-Winter’s Model brings both trend and seasonality into the equation. This can be analysed using either the multiplicative or additive method. In the additive version, seasonality is expressed as a quantity to be added to or subtracted from the series average. For the multiplicative model seasonality is expressed as a percentage (seasonal relatives or seasonal indexes) of the average (or trend).

These are then multiplied times values in order to incorporate seasonality. Associative Models Also known as “causal” models involve the identification of variables that can be used to predict another variable of interest. They are based on the assumption that the historical relationship between “dependent” and”independent” variables will remain valid in future and each independent variable is easy to predict. This form of analysis can take several months and is used for medium-term forecasts for products in their growth or maturity phase.

The procedure for this model is to collect several periods of history relating to the independent and dependent variables themselves, establish the relationship that minimizes mean squared error of forecast vs actual using linear or non-linear and singular or multiple regression analysis. So you first predict the independent variable, then look at the established relationships between that independent variable and the dependent ones to predict what the dependent variables will be. You then develop an equation that summarizes the effects of predictor variables.

To do this you will need aggregate data which is not always readily available and this model can be become overly complex the more factors are included as variables. Examples of the relationship between independent and dependent variables include: interest rates will impact on home loan applications, soil conditions will effect crop yields, location and size of land will effect sales levels. Techniques Linear regression, the objective is to develop an equation that summarizes the effects of the predictor (independent) variables upon the forecasted (dependent) variable.

If the predictor variable were plotted, the object would be to obtain an equation of a straight line that minimizes the sum of the squared deviations from the line (with deviation being the distance from each point to the line). Where there is more than one predictor variable or if the relationship between predictor and forecast is not linear, simple linear regression wont be adequate. For multiple predictors, multiple regression should be used, while non-linear relationships needs the use of curvilinear regression.

Econometric forecasting Uses complex mathematical equations to show past relationships between demand and variables that influence the demand. An equation is derived and then tested and fine-tuned to ensure that it is as reliable a representation of the past relationship as possible. Once this is done, projected values of the influencing variables (income, prices, etc. ) are inserted into the equation to make a forecast. An example of this is the ARIMA model (autoregressive integrated moving-average). NB Box and Jenkins proposed a three stage methodology: model identification, estimation and validation.

This involves identifying if the series is stationary or not and the presence of seasonality by examining plots of the series, autocorrelation and partial autocorrelation functions. Then models are estimated using non-linear time series or maximum likelihood estimation procedures. Finally validation is carried out with diagnostic checking such as plotting the residuals to detect outliers and evidence of model fit. Evaluating Forecasts – determined by computing the bias, mean absolute deviation (MAD), mean square error (MSE), or mean absolute percent error (MAPE) for the forecast using different values for alpha.

Bias is the sum of the forecast errors. These measures give more accuracy to the forecast of bias by taking into account the impact of over-forecasting and under-forecasting on the results. Choosing a method for different organisations/purposes No single technique works in every situation but the two most important factors are cost and accuracy. Other factors to consider are availability of historical data and the time & resources needed to gather and analyse the data as well as the timeline of the forecast – how far into the future you are trying to look. Often an organisation can use several methods for different purposes.

For example a charitable organisation might lack funds & technology but usually keep excellent records of their history and there is a multitude of readily accessible socio-economic data that can be applied to identify patterns and behaviours. They are also usually looking at predicting the situation for the next year or three years depending on their funding cycles and do not have months to spare while they determine variables. In this discussion of a state energy boards forecasting options (see link to pdf) they discuss the use of several methods depending on what they are trying to achieve.