Nickel case illustrates the importance of forecasting. Remember: successful firms are constantly engaged in long term strategic planning, even 10 years in future, which involves forecasting.
Example: FDA approval.
FORECASTING WITH TIME-SERIES MODELS
Using historical, time-series data to forecast (predict) the future, i.e. extrapolate past trends into the future. Examples: Using time-series data for GDP, auto sales, interest rates, stock prices to predict the future. Possible limitation of time-series forecast?
Decomposing Time-Series Patterns (Behavior over time):
Four categories: Trend, Cycles, Seasonality, Random shocks
1. Trend (secular component). Long-run trend in a variable, e.g. real GDP has grown at 3% rate since WWII, CPI by about 4%, M1 by 5%, S&P500 by 12%, etc. Could decrease: no. of farmers, manufacturing share of economy, union membership, etc. See p. 185 Figure 5.1.
2. Cycle. Cyclical movement around the trend, e.g. the 10 business cycles in the
3. Seasonal patterns, depending on the time of year or "season." Seasonal variation around either the trend or cycle. Examples of seasonality?
Economic data are either: a) NSA (not seasonally adjusted) or b) SA (seasonally adjusted).
4. Random fluctuations, or shocks, i.e. unpredictable, irregular, unexplained variation. Even the most accurate, sophisticated economic model cannot account for, or predict, random fluctuations. The "errors" (predicted - actual) from a regression are partly due to random fluctuations.
The importance of the trends, cycles, seasonality and randomness depends on the time-series variable and the length of time considered. Examples: sales of breakfast cereal or toothpaste vs. new vehicles or Xmas toys or golf clubs. Construction employment vs. retail. Daily sales of cars versus annual sales over thirty years.
FITTING A SIMPLE TREND
See p. 187 Figure 5.2, plot of annual sales over time. SLS = f (Time). No obvious seasonality or cycle, minimum random fluctuations are small. We start by estimating a linear trend:
Qt = a + b t,
where Q = annual sales, and t = time trend, where:
YR t___
1990 1
1991 2
1992 3
etc...
OLS results: Qt = 98.2 + 8.6 t
Interpretation: As t goes up by one unit (one year), SLS goes up by 8.6 (units or dollars?).
Alternative model: Qt = a + b t + c t2. Interpretation:
If c is insignificant (not different from 0), the trend is linear.
If c is pos and significant, the growth is exponential, SLS grow at an increasing rate.
If c is neg. and significant, SLS grow over time, but at a decreasing rate.
OLS: Qt = 101.8 + 7.0 t + .12 t2
T-statistics indicate that all coefficients are pos and significant, indicating that the quadratic specification is a better fit, panel b on p. 187.
Forecasting with the OLS equations for YR. 13:
Linear: Q13 = 98.2 + 8.6 (13) = 210.0
Quadratic: Q13 = 101.8 + 7 (13) + .12 (13)2 = 213.08
PROBLEM: Check Station 1 on p. 189:
$50 (1.05)35 =
$50 (1. 06)35 =
Using Time-series Lags:
We can also specify an OLS model using past observations, such as:
Qt = a + b Qt-1 + c Qt-2 + d Qt-3 +.... Qt-n .......where n = number of lags.
Estimate OLS, see if the coefficients (a, b, c...) are significant, determine the appropriate number of lags.
Using lags to model time-series: GDP, IP, CPI, SLS, etc.
CHECK STATION 2: ACt = .3 + .6 ACt-1 and current AC = $2.00. Predict AC for the next 3 quarters.
CASE STUDY: DEMAND FOR TOYS, p. 192-193. 40 quarters of time-series sales data. t = 1 for Winter 1995, t = 2 for Spring 1995, etc.
OLS: Qt = 141.16 + 1.998 t and note that the t-stat > 2, so time is statistically significant.
Forecast for Q = 41, Q41 = 141.16 + 1.998 (41) = 223.08
Issue for toy sales: seasonality. What to do? Check forecast error by season, using data on p. 195:
Actual Fall SLS: +20.78 above predicted time trend.
Actual Winter SLS: -17.03 below trend.
Actual Spring SLS: -3.53 below trend.
Actual Summer SLS: .22 below trend.
Model under predicts Fall SLS, over predicts Winter, Spring and Summer SLS. We can then adjust forecast for Q41 by subtracting -17.03 from the trend line prediction: 223.08 - 17.03 = 206.05.
Another method to adjust for seasonality: add Dummy Variables (0 or 1) to the model:
Period Dummy Variable
W S U F
Winter 95 1 0 0 0
Spring 95 0 1 0 0
Summer 95 0 0 1 0
Fall 95 0 0 0 1
Winter 96 1 0 0 0
etc...
Model: Qt = b t + c W + d S + e U + f F
OLS: Qt = 1.89 t + 126.24W + 139.85 S + 143.26 U + 164.38 F
For Winter 2005 (Q41) we have: Q = 1.89 (41) + 126.24 (1) = 203.73.
BAROMETRIC MODELS
Using leading indicators to forecast, e.g. building permits are a leading indicator of future housing construction, stock market is a leading indicator of future economic activity, consumer confidence as a leading indicator of auto sales, etc.
Example: Index of Leading Economic Indicators, a composite index of ten economic variables used to predict future economic conditions, one of the most closely watched economic variables. Released monthly by The Conference Board in NYC (also releases "coincident index" and "lagging index"), it has been fairly accurate at predicting recessions, but has also falsely predicted several recessions. Variables are selected that "lead" the general business cycle, turn down ahead of recessions and turn up ahead of expansions such as:
1. Weekly manufacturing hours
2. Manufacturers new orders
3. Plant and equipment orders
4. Unemployment claims
Logic: manufacturing/production leads retails sales (coincident variable).
5. Building permits
6. Money supply
7. Interest rate spread
8. SP500 Index
See full description at http://www.conference-board.org, The Conference Board's web page.
ECONOMETRIC MODELS
System of equations that attempts to accurately model the key economic variables, in a "structural model" of the micro or macro economy. Large macro models have over 1000 equations and variables that attempt to model and estimate GDP.
Advantage of econometric models: Complete quantitative description of the structure of the economy that captures the interdependence of economic variables, i.e. the feedback effects and feedback loops. Example: production by a firm depends on consumption, which depends on income, which depends on wages and the level of employment, which depends on production.
The sophisticated nature of econometric models, in contrast to a single equation model, could potentially lead to more accurate forecasts, see example p. 198.
Forecasting Accuracy
To quantitatively measure forecast accuracy, the RMSE (p. 203) is most often used:
RMSE =
where Q = actual value, Q* = forecast value, m = # of forecasts, and k = number of estimated variables. The lower the RMSE, the better the forecast. Note that the numerator is "sum of the squared errors" and the denominator is the "degrees of freedom."
Forecast errors could be due to:
1. Random errors
2. Equation misspecification
3. Omitted variables, etc.
Evidence/research on forecast accuracy - Stephen McNees at Boston Fed has conducted ongoing research on forecast accuracy. Conclusions:
1. Forecast accuracy has improved over time due to better data and better models; improvements and advances in computers, software and statistical procedures, at least for some variables.
2. Some economic variables remain extremely hard to forecast accurately, such as???
3. Short term forecasts are more accurate than long term.
4. There is no single best forecaster or forecast model that is consistently best over time.
Nickel Forecast: What about the nickel company's forecast, see p. 204?
Growth in nickel production/sales was strong in the 1980s, but then was weak, and declined in the early and mid-1990s due to recessionary conditions in US (1990-1991), Europe (1991-1994), Mexican currency crisis (1994), and the Asian currency and financial crisis (1997-1998), which put downward pressure on nickel prices ($9,000/ton to $6000/ton). In addition, two of the firm's competitors also expanded production, and none was profitable. The firm's failed expansion and accompanying problems resulted from both bad luck and bad forecasting.
