OPRE 3333 Chapter 8

Moving averages Forecast

Uses the average of the most recent K data values in the time series as the forecast for the next period.

Naive Forecasting Method

Using the most recent data to predict future data.

Trend pattern

shows gradual shifts or movements to relatively higher or lower values over a longer period of time.

Smoothing constant

(a) is the weight given to the actual value in period t; weight given to the forecast in period t is 1-a

Trend is usually a result of long-term factors

- Population increases or decreases. -Shifting demographic characteristics of the population. -Improving Technology -Changes in the competitive landscape. -Changes in consumer preferences

Identifying Time Series Patterns

-The Underlying pattern in the time series is an important factor in selecting a forecasting method. -Use time series plot -We need to use a forecasting method that is capable of handling the pattern exhibited by the time series effectively.

Time Series

A sequence of observations on a variable measured at successive points in time or over successive periods of time. Measurements taken at regular interval. The pattern of the data is important.

Mean Absolute Percentage Error (MAPE)

Average of the absolute value of percentage forecast errors.

Trend-Cycle effects

Cyclical effects and long-term trend effects combined.

Cyclical Pattern

Exists if the time series plot shows an alternating sequence of points below and above the trend line lasting more than one year.

Horizontal Pattern

Exists when the data fluctuate randomly around a constant mean over time.

Forecast Accuracy

Insight into choosing a good value for (a) can be obtained by rewriting the basic exponential smoothing model as: look at ppt -if the time series contains substantial random variability, a small value of the smoothing constant is preferred and vice-versa. -Choose the value of (a) that minimizes the MSE.

Mean Absolute Error (MAE)

Measure of forecast accuracy that avoids the problem of positive and negative forecast errors offsetting one another.

Time series analysis

Objective method of forecasting that relies on the analysis of historical data to develop a prediction for the future.

Forecasts (Qualitative & Quantitative)

Qualitative methods: generally involve the use of expert judgement to develop forecasts Quantitative methods can be used when: -Past information about the variable being forecast is available. -The information can be quantified. -It is reasonable to assume that past

Mean Forecast Error (MFE)

Running sums of forecast / number of observations This tells you on average if you are high or too low. Negative # is OVER forecasting Positive # is UNDER forecasting

Trend and Seasonal Pattern

Some time series include both a trend and a seasonal pattern.

Forecast Accuracy

The values of the three measures of forecast accuracy for the 3 week moving average calculations.

Exponential smoothing

Uses a weighted average of past time series values as a forecast

Stationary Time Series

it denotes a time series whose statistical properties are independent of time: -The process generating the data has a constant mean. -The Variability of the time series is constant over time. Time series plot will always exhibit: horizontal pattern with random fluctuations

Mean Squared Error (MSE)

measure that avoids the problem of positive and negative errors offsetting each other is obtained by computing the average of the squared forecast errors.

Seasonal pattern

recurring patterns over successive periods of time. The time series plot not only exhibits a seasonal pattern over a one-year period but also for less than one year in duration. Basically the plot can be used to represent smaller periods than year.

forecast error

the difference between a forecast and the actual demand ^ e. = y - y t. t t Topics: •Forecast error. •Mean forecast error (MFE). •Mean absolute error (MAE). •Mean squared error (MSE). •Mean absolute percentage error (MAPE).

Linear Trend Projection

•Regression analysis can be used to forecast a time series with a linear trend. •Simple linear regression analysis yields the linear relationship between the independent variable and the dependent variable that minimizes the MSE. •Use this approach to find a best-fitting line to a set of data that exhibits a linear trend. The Variable to be forecasted (yt, the actual value of the time series period t) is the dependent variable. •Trend variable (time period t) is the independent variable.