Forecasting

1

• Forecasting
• Basic Concepts
• And
• Stationary Models

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What is Forecasting?

• Forecasting is the process of predicting the
  future.
• Forecasting is an integral part of almost all
  business enterprises including
• Manufacturing firms that forecast demand for
  their products, to schedule manpower and raw
  material allocation.
• Service organizations that forecast customer
  arrival patterns to maintain adequate customer
  service.
• Security analysts who forecast revenues, profits,
  and debt ratios, to make investment
  recommendations.
• Firms that consider economic forecasts of
  indicators (housing starts, changes in gross
  national profit) before deciding on capital
  investments.

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Benefits of Forecasting

• Good forecasts can lead to
• Reduced inventory costs
• Lower overall personnel costs and increased
  customer satisfaction
• A higher likelihood of making profitable
  financial decisions
• A reduced risk of untimely financial decisions

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How Does One Prepare a Forecast?

• The forecasting process can be based on
• Educated guess.
• Expert opinions.
• Past history of data values, known as a time
  series.

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Components of a Time Series

• Long-term Trend Effects
• Long-term trend is typically modeled as a linear,
  quadratic or exponential.
• A time series that does not exhibit any trend
  over time is a stationary model.
• Seasonal Effects
• When a predictable, repetitive pattern is
  observed, the time series is said to have
  seasonal effects.
• Seasonal effects can be associated with
  calendar/climatic changes or tied to yearly,
  quarterly, monthly, etc. data
• Cyclical Effects
• An unanticipated temporary upturn or downturn
  that is not explained by seasonal effects are
  said to be cyclical effects.
• Cyclical effects can result from changes in
  economic conditions.
• Random Effects

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ExampleMotorhome Sales 1975-2000
Seasonal Effects Qtr 4 Lower than qtr 3 Qtr 3
Higher than qtr 2 Qtr 2 Higher than qtr 1 Qtr 1
Higher than qtr 4
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Steps in the Time Series Forecasting Process

• The goal of a time series forecast is to identify
  factors that can be predicted.
• This is a systematic approach involving the
  following steps.
• Step 1 Hypothesize a form for the time series.
• Collect historical data and graph the data vs.
  time.
• Hypothesize and statistically verify a form for
  the time series.
• Step 2 Select a forecasting technique from a
  set of possible methods for the form of the
  time series.
• Statistically determine which method best
  forecasts the data.
• Step 3 Prepare a forecast.

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Stationary Forecasting Models

• A stationary model is one that forecasts a
  constant time series value over time.
• The general form of such a model is

yt b0 et
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Determining if a Stationary Model Is Appropriate

• Is there trend?
• Use Linear Regression -- Check the p-value for ?1
• Is there seasonality?
• Visually check of time series graph
• Autocorrelation measures the relationship between
  the values of the time series every k periods
  this is called autocorrelation of lag k.
• There are tests for doing this, but we will just
  do a visual check.
• Lag 7 autocorrelation indicates one week
  seasonality (daily data) lag 12 autocorrelation
  indicates 12-month seasonality (monthly data),
  etc.
• Are there cyclical effects?
• Visually check of time series graph.

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Moving Averages

• There are t observations y1 (oldest), y2, y3, ,
  yt (most recent)
• In stationary forecasting models, the forecast
  for the constant value, ß0, for the next time
  period t1, Ft1, is the average (or a weighted
  average) of 1 or more of the immediately prior
  observations, yt, yt-1, etc.
• Since the time series is stationary, this
  forecast for time period t1, will be the
  forecast for all future periods t2, t3, etc.
• The forecast changes only after more data is
  collected.

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Moving Average Methods

• Last Period
• Ft1 yt
• Use the last observed value of the time series
• n period Moving Average
• Ft1 (yt yt-1 yt-n1)/k
• Average the last n observed values of the time
  series
• n period Weighted Moving Average
• Ft1 wtyt wt-1yt-1 wt-n1yt-n1
• Weight the last n observed values (the ws sum to
  1)
• Exponential Smoothing (Discussed in another
  module)
• All observations are weighted with decreasing
  weights

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Example

• Galaxy Industries needs to forecast weekly demand
  for the next three weeks for its Yoho brand yoyo
  based on the past 52 weeks demand. If demand is
  deemed to be stationary, use
• Last Period Technique
• 4-Period Moving Average Technique
• 4-Period Weighted Moving Average Technique (.4,
  .3, .2, .1)

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Time Series For the Past 52 Weeks
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Determining if the Model Is Stationary

• Graph the time series.

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Using Regression to Test for Trend
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Using Regression to Test for Trend
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Is Linear Trend Present?

• Check p-value for ß1.

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Forecasts

• Since we have concluded that this is a stationary
  model, we can use moving average methods.
• Last Period
• Since model is stationary, F55 F54 F53 484
• 4 Period Moving Average
• Since model is stationary, F55 F54 F53 401
• 4 Period Weighted (.4, .3, .2, .1) Moving
  Average
• Since model is stationary, F55 F54 F53 441.3

F53 y52 484
F53 (y52 y51 y50 y49)/4 (484 482
393 245)/4 401
F53 .4y52 .3y51 .2y50 .1y49 .4(484)
.3(482) .2(393) .1(245) 441.3
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EXCEL Last Period

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Excel Moving Average Forecast

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Excel Weighted Moving Average

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Review

• Possible Factors in a Time Series Model
• Trend, Seasonal, Cyclical, Random Effects
• Determining if the Time Series is Stationary
• No noticeable seasonal or cyclical effects on
  time series plot
• Use Regression to test for ß1 0
• High p-value (No trend stationary)
• Moving Average Forecasting Methods
• Last Period, Moving Average, Weighted Moving
  Average, Exponential Smoothing
• Forecasts for next period will be the forecasts
  for all future periods until additional time
  series values occur
• Excel approach