Forecasting

Contents
Forecasting
Forecasting Methods
  • Expert Opinion
  • Prediction Markets
    • Prediction is based on the opinions of participants investing in a prediction market, such as the Iowa Electronic Markets
  • Time Series Forecast
    • A time series forecast is based on a single time series, a sequence of values of a variable over time.
  • Regression
    • Regression is a statistical method for finding an equation (function, line) that predicts a predicted (dependent) variable from predictor (independent) variables.
  • Forecasting Model
    • A forecasting model is a computer program that generates predictions based on evidential links among variables.
    • Models predict climate, weather, the economy, effects of proposed legislation, epidemics, elections, hurricanes, military strategies, investments, sports.
Kinds of Predictions
  • Point
    • Single value, typically with a margin of error
    • Biden wins 329 electoral votes
  • Range
    • Range of values, typically with a confidence level
    • Biden wins between 320 and 340 electoral votes
  • Probability
    • Probability of a single value
      • The probability Biden wins is 75 percent.
    • Probability of a range
      • The probability Biden gets at least 270 electoral votes is 60 percent.
    • Probability Distribution (538)
      • The probability Biden wins is a probability distribution that looks like:

Times Series Forecast, Example

A time series forecast is based on a single time series

FRED Graph of Real Disposable Personal Income
Time Series Forecast of Real Disposable Personal Income
  • Mathematica
    • fred = ServiceConnect[“FederalReserveEconomicData”]
    • tsm = TimeSeriesModelFit[fred[“SeriesData”, “ID” -> {“DSPIC96”}]]
      • ARIMAProcess [-0.0262876, {0.168011, -0.0264697, -0.0142413}, 2, {-1.54527, 0.562182}, 10186.4]
    • ListLinePlot[{tsm[“TemporalData”], TimeSeriesForecast[tsm, {24}]}, PlotRange -> {{3.4*10^9, 3.9*10^9}, {10000, 19000}}]
Two-year Forecast of Real Disposable Personal Income using ARIMA
Regression, Example

Regression is a statistical method for finding an equation (function, line) that predicts a predicted (dependent) variable from predictor (independent) variables.

Data and Regression
  • The objective is to predict the Price of a used car based on Age.
    • Price is the predicted variable
    • Age is the predictor variable
  • The Mathematica command LinearModelFit calculates the regression:
    • lm = LinearModelFit[data, x , x]
  • The result is the formula:
    • Price = 7836.26 – (502.425 x Age) 
  • The formula predicts, for example:
    • Price of car Age 4 = 5826.56
    • Price of car Age 6 = 4821.71
    • Price of car Age 10 = 2812.01

Graph of Price against Age
Dots represent Data Points
The Line represents: Price = 7836.26 – (502.425 x Age) 
Forecasting Model, Examples

A forecasting model is a computer program that generates predictions based on evidential links among variables.

Monty Hall Simulation

To solve the famous probability problem, the Monty Hall Simulation plays the Monty Hall game a million times.

View Monty Hall Simulation

Nest Egg Forecast

The Nest Egg Forecast estimates how long your retirement funds will last.

View Nest Egg Forecast

Joint Committee on Taxation
  • The Joint Committee on Taxation (JCT) is a nonpartisan, congressional agency responsible for providing the U.S. Congress with the budgetary effects of all tax legislation.
  • From JCT’s Overview Of Revenue Estimating Procedures And Methodologies
    • “The largest model used by the Joint Committee staff is the individual model, a model based on a stratified sample of individual tax returns submitted to the IRS. A tax model simulation works by applying the tax laws and parameters to each return on the sample to recreate that return’s Federal individual income tax liability for a given year. The model generally assumes that taxpayers make optimal choices regarding such decisions as claiming itemized deductions or claiming credits. Then, by changing rules or parameters reflected by a tax proposal, each return’s liability is recalculated. This produces an estimated change in liability for that proposal.” 
Congressional Budget Office
  • The Congressional Budget Office (CBO) is a “strictly nonpartisan” federal agency of the legislative branch that conducts objective, impartial “analyses of budgetary and economic issues to support the Congressional budget process
  • Seven Things to Know About CBO’s Analyses
    • The analyses involve regular use of hundreds of models and other estimating techniques. For example, the agency estimated the effects of the ACA on the labor supply in its economic projections mainly by calculating the effects of the law on marginal and average tax rates and drawing upon research about changes in the labor supply resulting from changes in tax rates.
Covid-19

Election Forecasting Sites
FiveThirtyEight 2020 Election Forecasting Model
projects.fivethirtyeight.com/2020-election-forecast/
Overview
  • The FiveThirtyEight model runs 40,000 simulations, tallying how many electoral votes the candidates get in each run. Probabilities are determined by counting simulations. For example, if Biden gets at least 270 electoral votes in 26,000 simulations, his probability of winning is 26,000/40,000 = 65 percent.
  • The model weighs:
    • state polls
    • how a state voted in the last two presidential elections
    • whether the state is home to the presidential or vice presidential candidate
    • how easy it is to vote in the state
    • economic conditions (jobs, personal income, personal spending, manufacturing, inflation, stock market)
    • uncertainty, including how much polling error is correlated across states regarding:
      • Race, Religion, Latitude and longitude, Region (North, South, Midwest, West), Urbanization, Median household income, Median age, Gender, Education, Immigration,  COVID-19 severity index, expected vote by mail .
Procedure
  • FiveThirtyEight combines polling averages, demographics, and past voting patterns to generate an Enhanced Snapshot of each state.
  • The Enhanced Snapshots are combined with economic predictions and incumbency advantage to make Predictions of Vote Share for each state.
  • The state Predictions of Vote Share, factored by uncertainties, are used to compute, for each n from 0 to 538, how probable each candidate is to win n electoral votes. The computation comprises 40,000 simulations.
  • The Electoral Vote Probabilities are used to predict the probabilities that each candidate will get at least 270 electoral votes.
  • The Electoral Vote Probabilities are also used to calculate the expected electoral votes for each candidate
    • Expected electoral votes = the sum, for each n from 0 to 538, of the probability of the candidate winning n electoral votes times n.
Flowchart for FiveThirtyEight 2020 Election Forecast
Details
  • Adjustments
    • Likely voter adjustment
    • House effects adjustment
    • Timeline adjustment
  • Demographics + Past Voting Patterns
    • How the state voted in the past two presidential elections compared with the national average.
    • Whether the state is home to the presidential or vice presidential candidate
    • How easy it is to vote in the state, based on the Cost of Voting Index
      • States with higher barriers to voting tend to produce better results for Republican candidates and states with lower barriers tend to lean more Democratic.
  • Economic Conditions
  • Uncertainty
    • National drift
      • How much the overall national forecast could change before Election Day
    • Election Day error
      • How much the final forecast of the national popular vote could be off on Election Day
    • Correlated state error
      • How much polling error is correlated across states regarding:
        • Race, Religion, Latitude and longitude, Region (North, South, Midwest, West), Urbanization, Median household income, Median age, Gender, Education, Immigration,  COVID-19 severity index, expected vote by mail 
    • State-specific error
      • How much the state prediction could be off on Election Day
Prediction of Texas Vote Share
But Nate, you were wrong in 2016.