Forecasting Tools in AGEC 622

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Forecasting Tools in AGEC 622

• Trend
• Linear and non-linear
• Multiple Regression
• Seasonal Analysis
• Moving Average
• Cyclical Analysis
• Exponential Smoothing
• Time Series Analysis
• Read Chapter 16 of Simulation book
• Read first half of Chapter 15
• Read journal article Including Risk in Economic
  ..

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Forecasting Tools

• One BIG difference in what we do and what other
  forecasters do
• We assume the forecast is not a point estimate
• We do probabilistic forecasting about the
  deterministic forecast
• In other words we assume there is risk about the
  point forecast, which is not know with certainty

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Probabilistic Forecasting
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Role of a Forecaster

• Analyze historical data series to quantify
  patterns that describe the data
• Extrapolate the pattern into the future for a
  forecast using quantitative models
• In the process, become an expert in the industry
  to identify structural changes before they are
  observed in the data incorporate new
  information into forecasts
• In other words, THINK
• Look for the unexpected

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Define Data Patterns

• A time series is a chronological sequence of
  observations for a particular variable over fixed
  intervals of time
• Daily
• Weekly
• Monthly
• Quarterly
• Annual
• Six patterns for time series data (data we work
  with is time series data because use data
  generated over time.)
• Trend
• Cycle
• Seasonal variability
• Structural variability
• Irregular variability
• Black Swans

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Patterns in Data Series
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Trend Variation

• Trend a general up or down movement in the values
  of a time series over the historical period of
  observation
• Most economic data contains at least one trend
• Increasing, decreasing or flat trends
• Trend represents long-term growth or decay
• Trends caused by strong underlying forces, such
  as
• Technological changes
• Change in tastes and preferences
• Change in income and population
• Market competition
• Inflation and deflation
• Policy changes

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Cyclical Variation

• Cycle is a recurring up and down movement around
  a trend
• Cycles persist for 2 to 20 years from peak to
  peak
• Business cycle is most notorious
• Agriculture examples are cattle and hog cycles
• Two components to a cycle
• Expansion
• Contraction
• Cycles caused by
• Changes in tastes and preferences
• Economic activity (inflation and deflation)
• Production cycles (animals)
• Tides and sunspots?
• Cycles vary in length and magnitude

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Seasonal Variation

• Periodic (cyclical) patterns in a time series
  that complete the cycle within a year
• Caused by
• Weather, seasons of the year
• Production/marketing patterns
• Customs and holidays
• Agricultural production causes seasonal variation
  of prices
• Holidays cause retail demand and sales to vary on
  a seasonal pattern
• Thanksgiving turkey
• Easter ham
• Winter cheese
• Summer ice cream
• Gasoline sales summer vacation
• Holidays and high temperatures crushed ice

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Structural Variation

• Variables you want to forecast are often
  dependent on other variables
• Qt. Demand f( Own Price, Competing Price,
  Income, Population, Season, Tastes Preferences,
  Trend, etc.)
• Y a b (Time)
• Structural models will explain most structural
  variation in a data series
• Even when we build structural models, the
  forecast is not perfect
• A residual remains as the unexplained portion

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Irregular Variation

• Erratic movements in time series that follow no
  recognizable regular pattern
• Random or stochastic movements
• Risk is the non-systematic variability in the
  residuals
• Leads to Monte Carlo simulation of the risk in
  our probabilistic forecasts
• Recognize risks cannot be forecasted
• Incorporate risks into probabilistic forecasts
• Provide forecasts with confidence intervals

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Black Swans (BSs)

• BSs low probability events
• Is an outlier, outside realm of reasonable
  expectations
• Carries an extreme impact
• Human nature causes us to concoct explanations
• Black swans are an example of uncertainty
• Uncertainty is generated by unknown probability
  distributions
• Risk is generated by known distributions
• Current recession is a BSs
• A depression is a BSs
• Dramatic increases of grain prices in 2006 and
  2007

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Simplest Forecast Method

• Mean is the simplest forecast method
• Deterministic forecast of Mean
• Y ? ? Yi / N
• Forecast error (or residual)
• êi Yi Y
• Standard deviation of the residuals is the
  measure of the error (risk) for this forecast
• se (?(Yi Y)2/ (N-1)1/2
• Probabilistic forecast
• ? Y ?
• where ? represents the stochastic (risky)
  residual and is simulated from the êi resuduals

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Second Forecast Method -- Trend

• Trend is the underlying change in the data over
  an extended time period
• Trends change due to structural changes in the
  industry due to
• Policy changes
• Technology
• Tastes and preferences
• Trends can be linear and non-linear

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Linear Trend Forecast Models

• Deterministic trend model
• Yt a b Tt
• where Tt is time variable, T 1, 2, 3,
• Estimate parameters for model using OLS
• Multiple Regression in Simetar is preferred, it
  does more than estimate a and b
• Std Dev residuals Std Error Prediction (SEP)
• When available use SEP as the measure of error
  (stochastic component) for the probabilistic
  forecast
• Probabilistic forecast of a trend line becomes
• ?t Yt ?
• Which is rewritten using the proper
  specification for ?
• ?t Yt SEPt NORM()

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Non-Linear Trend Forecast Models

• Deterministic trend model
• Yt a b1 Tt b2 Tt2 b3 Tt3
• where Tt is time variable, T 1, 2, 3,
• Estimate parameters for model using OLS
• Probabilistic forecast from trend becomes
• ?t Yt SEPt NORM()

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Steps to Develop a Trend Forecast

• Plot the data
• Identify linear or non-linear trend
• Develop T, T2, T3 if necessary
• Estimate trend model using OLS
• Low R2 is usual
• F ratio and t-test will be significant if trend
  is statistically present
• Simulate model using Yt and SEPt
• Report probabilistic forecast

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Example of Linear Trend Model

• F-test, R2, t-test and Prob(t) values
• Prediction and Confidence Intervals

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Confidence Intervals in Simetar
Beyond the historical data you will find SEP
values in column 4 Y values in column 2 ? values
in column 1
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Meaning of the CI and PI

• CI is the confidence for the forecast of Y
• When we compute the 95 CI for Y by using the
  sample and calculate an interval of YL to YU we
  can be 95 confident that the interval contains
  the true Y0. Because 95 of all CIs for Y
  contain Y0 and because we have used one of the CI
  from this population.
• PI is the confidence for the prediction of Y
• When we compute the 95 PI we call a prediction
  interval successful if the observed values
  (samples from the past) fall in the PI we
  calculated using the sample. We can be 95
  confident that we will be successful.

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Non-Linear Trend Regression

• Add square and cubic terms to capture the trend
  up and then the trend down

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Is a Trend Forecast Enough?

• If we have monthly data, the seasonal variability
  will overwhelm the trend variability, so final
  model will need both trend and seasonal terms
  (See the Demo for Lecture 1 MSales worksheet)
• If we have annual data, cyclical or structural
  variability may overwhelm trend so need a more
  complex model
• Bottom line
• Trend is where we start, but we generally need a
  more complex model