Use Forecasting Basics to Predict Future Conditions

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y J. DeLayne Stroud

Basic terminologies of time series and forecasting can be difficult to understand. There are four basic learning points:

1. The definition of forecasting
2. Forecasting as a business and communicative process (not a statistical tool)
3. General definitions used in forecasting (regardless of statistical tool)
4. The statistical/mathematical techniques

Becoming Aware of the Broad View of Forecasting: Overview – Applications and Basic Steps

Forecasting is the prediction of future events and conditions and is a key element in service organizations, especially banks, for management decision-making. There are typically two types of events: 1) uncontrollable external events – originating with the national economy, governments, customers and competitors 2) controllable internal events – e.g., marketing, legal, risk, new product decisions within the firm.

The need for forecasting stems from the time lag between awareness of an impending event or need and the occurrence of that event. Organizations constantly try to predict economic events and their impact.

Following are a few applications for forecasting modules:

• Forecasting utilization rates for credit cards: build a model based on historical data and use the model to score a current credit card portfolio to determine utilization rates
• Model loss rates of a group of home equity lines of credit as a function of time
• An independent system operator, organized for monitoring the electrical grid, has a need to predict electrical usage – the volatility of the daily usage can be thought of as a blend of day-ahead-market volatility and monthly volatility, where the month can be one or more months forward

There are some basic steps for creating a forecast:

• Define the problem. How will the forecasts be used, who needs the forecast and what is the voice of the customer (VOC)?
• Gather the necessary information by obtaining historical (mathematical) data and utilizing the accumulated judgment and expertise of key personnel.
• Determine what graphical plots will best benefit management and design a preliminary analysis. Include descriptive statistics.
• Choose and fit models by using and evaluating a forecast model for decision making. Forecast errors and management response.

Forecasting System

A forecasting system consists of two primary functions: forecast generation and forecast control. Forecast generation includes acquiring data to revise the forecasting model, producing a statistical forecast and presenting results to the user. Forecast control involves monitoring the forecasting process to detect out-of-control conditions and identifying opportunities to improve forecasting performance. Figure 1 shows a visualization of a forecasting system and process.

Figure 1: Forecasting System

Forecasting Terminology

There are a number of common terms when discussing forecasting models:

• Point forecast: a single number that represents the best prediction (or guess)
• Prediction interval forecast: an interval (or range) of numbers that the actual value will be contained within – provides the “best” and “worst” case estimates of forecasts
• Out-of-sample (ex-ante forecasts), cross-sectional and time series data: refers to data used to validate the forecasting model and compares forecasted values to the out-of-sample data. Conversely, in-sample data refers to the data used to construct the model. Users should fit the model to the in-sample data.
• Out-of-sample data selection: data sets used to validate forecasts can be obtained in several ways:
  • Hold out x percent of most recent (rule of thumb is 10 percent) – usually for longitudinal data
  • Hold out x percent but randomly throughout the entire data set – usually for cross-sectional data
  • Use all data and wait for future values:
    • Cross-sectional data (regression techniques) where all observations are from the same time
    • Time series data (signal/noise techniques): a chronological sequence of observations

Forecasting Measures of Errors

In any forecasting, it is the accuracy – or “goodness of fit” – of future forecast(s) that is most important. There are three commonly used statistical measures used in forecasting: 1) mean absolute percentage error (MAPE), 2) mean absolute deviation error (MAD or MADeviation) and 3) predicted/mean squared deviation error (PMSE or MSDeviation).

If Y_t is the observed value at period t and F_t is the forecasted value at period t

Figure 2: Forecasting Formulas

Table 1: Examples of Forecast Error Measures
Period	Observed	Forecast	Abs Error	% Abs Error	Deviation2
1	138	150.25	12.25	8.9	150.06
2	136	139.50	3.5	2.6	12.25
3	152	157.25	5.25	3.5	27.56
4	127	143.50	16.5	13.0	272.25
5	151	138.00	13	8.6	169.00
6	130	127.50	2.5	1.9	6.25
7	119	138.25	19.25	16.2	370.56
8	153	141.50	11.5	7.5	132.25
Totals			83.75	62.12%	1140.19

Figure 3: Time Series Patterns

• Time series patterns: common patterns are called horizontal (stationary), seasonal, cyclical, and trends
• Adjustments by number of days: some of the variation in a time series may be due to variation in the number of days (from 28 to 31) per month (e.g., trading days). Use the following formula to make this adjustment before doing any forecasting.