2 - Forecasting and Estimation Flashcards
What is a forecast?
Statements about future events, particularly future values of economic variables, based on past observations and theoretically grounded, objective methods. Forecasts apply particularly to variables that cannot or can barely be influenced by the instance in charge of forecasting.
What are the implications of forecasting errors?
faulty forecasts enable bad decisions
What forecasting errors are there?
over-forecast
- e.g. planning too much capacity or expecting too high cost
(glass half full)
under-forecast:
- turning down valuable customers or spending too much time or money
(glass more than full)
What kinds of forecast data are there?
Transaction data
Controls data
Historical forecast data
Auxiliary data
Kinds of forecast data
Transaction data
- units of capacity sold per product
- number of appointments serviced on time
Kinds of forecast data
Controls data
- appointment slots offered
- number of employees on shift
How much did we actually put on the market?
Kinds of forecast data
Historical forecast data
- expected service time
- forecasted demand
What did we estimate in the past?
Kinds of forecast data
Auxiliary data
- currency or tax data
- demographic information
- weather data
Additional data from other sources
Levels of aggregation
Design decision: How much to aggregate?
detailed information for finely tuned controls
vs.
few observations and small numbers
Examples:
Forecast appointment requests per day and service point?
Forecast appointment requests per week, expecting possible shifts?
Forecast travel times per month or day of the week?
-> aggregation depends on the data we have and the target we have
Forecasting methods - overview
What types of methods are there?
Ad-hoc or structural methods
time-series methods
Forecasting methods - overview
Ad-hoc or structural methods
- purely descriptive, based on historical observations of trends
- identify level, trend, seasonality
- e.g. m-period moving average, exponential smoothing
-> Returns a function to predict the next value from historical observations
Forecasting methods - overview
Time-series methods
- model an underlying dynamic system that generates data over time
- e.g. auto-regressive process, ARIMA
-> returns a model to predict the next value as resulting from the process - needs an estimation method to find the best model and its parameters
The simplest ad-hoc method
Simple moving average
compute the new forecast results by equally weighting the past n values
- every new observation enters the forecast
- the forecast evens out for all future instances
- strongly depends on the chosen n
Another ad-hoc method
Exponential smoothing
Parameter Alpha in [0 and 1] determines the weight of new observations
Alpha > 0,5: more emphasis on the latest observation
-> adapts quickly but is volatile
Alpha ≤ 0,5: more emphasis on history than on the latest observation
-> very stable but takes long to adapt
Alpha = 1: the naïve forecast - forecasts the value of the latest observation
-> a frequent benchmark
Time-series methods
Time-series forecasting in three steps
- make a hypothesis about the process generating the data
- estimate process parameters
- apply the best forecasting method for the model
In contrast to structural forecasting, time-series methods can exploit correlations in the data
Time-series methods
Common assumption
Stationarity
- statistical properties of process do not change over time (have to remove trend or seasonal patterns!)
- Example: Auto-regressive Process
Time-series methods
Example for non-stationary models
ARIMA (auto-regressive integrated moving average)
- can account for trend: probability distribution of the underlying process change over time
Estimation for Forecasting
Estimation vs. forecasting
Estimation:
- descriptive
- What has been observed?
- e.g. What price sensitivity do the bookings of the previous 12 months reveal?
Forecasting:
- predictive
- What will be observed?
- e.g. How will price sensitivity develop in the next 12 months?
Estimation approaches
What estimation approaches are there?
Non-parametric estimation
parametric estimation
Estimation approaches
Non-parametric estimation
- assumes no particular distribution or model (we don’t have any assumption, just looking at data)
- estimate the “shape” of observations
Example:
number of customers buying during a time slice
-> requires data on each time slice
Estimation approaches
Parametric estimation
- assumes an underlying distribution
- estimate relevant distribution/model parameters
Example:
Regression function deriving the expected number of customers from prices and days left in the sales horizon
Estimation approaches
Estimator
= “guessing” parameters that we assume created the observed data
- observed data: e.g. sales
- Parameters: e.g. demand model (for parametric estimation)
Estimation objectives
unbiased
efficient
consistent
Estimation objectives
unbiased
- expected value of the estimator equals the actual value of the parameter
- estimate is not systematically too high or too low
Estimation objectives
Efficient
- estimator is unbiased AND has as little variance as possible
- Cramer-Rao bound provides a lower bound on the variance
Estimation objectives
consistent
- estimator converges to the true value as the sample size increases
- increasing the number of observations provides better results
Estimation challenges
Endogeneity
Constrained observations
Small number of observations
Biased data
Estimation challenges
Endogeneity
explanatory variable is correlated with the error term
High prices lead to high demand?
Simultaneity: prices are driven by expected demand
Estimation challenges
Constrained observations
Observations are systematically censored
There were never more than 100 bookings?
The capacity never exceeded 100 units!
Estimation challenges
Small number of observations
Large samples more closely approximate the population
The previous three observations indicate an upward trend
- but can it be trusted?
Estimation challenges
Biased data
The sample systematically differs from the population
Data from the loyalty program indicates a high rate of repeat bookings - but not for all customers!
Minimum square error:
Linear regression
- predicting dependent variables based on independent variables
- “linear” regression assumes a linear relationship between dependent and independent variables: y=a*x+b
- a and b are calculated to minimize the square error across all observations
Regression Estimators are causal predictions
Advantages and disadvantages
Advantages:
- when the causal relationship is accurately defined, abrupt changes in the dependent variables can be explained
- a well fitting regression model helps to explain the behavior of the dependent variable
Disadvantages:
- it is difficult to correctly identify all relevant variables and relationships
- there can be a great number of independent variables
Regression Estimators for demand models: Variants
- assuming different shapes of the regression function
- i.e. to predict demand from functions of price and product characteristics
Regression Estimators for demand models: Variants
Kinds of variants
Probit
- probability of one event
- > such as buying or not buying
Multinomial logit/probit
- set of discrete probabilities
- > such as probabilistic product choice
Censored or “constrained” demand
- ideally we predict phenomena that we can fully observe (oil price, weather in April)
- sometimes we try to predict something that we cannot (yet) fully observe
- > average lifetime of frogs, when some are still alive
- > demand, when demand exceeds supply
- in these cases, observations are censored or “constrained”; we have to “unconstrain” sales to estimate demand
Censored or “constrained” demand
Simple unconstraining heuristic
If the product was not sold out:
- demand = sales
If the product was sold out
- demand = maximum(sales, previous forecast)
Related field: Survival analysis
