2 - Forecasting and Estimation Flashcards Preview

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Flashcards in 2 - Forecasting and Estimation Deck (37)
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1
Q

What is a forecast?

A

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.

2
Q

What are the implications of forecasting errors?

A

faulty forecasts enable bad decisions

3
Q

What forecasting errors are there?

A

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)

4
Q

What kinds of forecast data are there?

A

Transaction data
Controls data
Historical forecast data
Auxiliary data

5
Q

Kinds of forecast data

Transaction data

A
  • units of capacity sold per product

- number of appointments serviced on time

6
Q

Kinds of forecast data

Controls data

A
  • appointment slots offered
  • number of employees on shift

How much did we actually put on the market?

7
Q

Kinds of forecast data

Historical forecast data

A
  • expected service time
  • forecasted demand

What did we estimate in the past?

8
Q

Kinds of forecast data

Auxiliary data

A
  • currency or tax data
  • demographic information
  • weather data

Additional data from other sources

9
Q

Levels of aggregation

Design decision: How much to aggregate?

A

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

10
Q

Forecasting methods - overview

What types of methods are there?

A

Ad-hoc or structural methods

time-series methods

11
Q

Forecasting methods - overview

Ad-hoc or structural methods

A
  • 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

12
Q

Forecasting methods - overview

Time-series methods

A
  • 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

13
Q

The simplest ad-hoc method

Simple moving average

A

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
14
Q

Another ad-hoc method

Exponential smoothing

A

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

15
Q

Time-series methods

Time-series forecasting in three steps

A
  1. make a hypothesis about the process generating the data
  2. estimate process parameters
  3. apply the best forecasting method for the model

In contrast to structural forecasting, time-series methods can exploit correlations in the data

16
Q

Time-series methods

Common assumption

A

Stationarity

  • statistical properties of process do not change over time (have to remove trend or seasonal patterns!)
  • Example: Auto-regressive Process
17
Q

Time-series methods

Example for non-stationary models

A

ARIMA (auto-regressive integrated moving average)

- can account for trend: probability distribution of the underlying process change over time

18
Q

Estimation for Forecasting

Estimation vs. forecasting

A

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?
19
Q

Estimation approaches

What estimation approaches are there?

A

Non-parametric estimation

parametric estimation

20
Q

Estimation approaches

Non-parametric estimation

A
  • 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

21
Q

Estimation approaches

Parametric estimation

A
  • 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

22
Q

Estimation approaches

Estimator

A

= “guessing” parameters that we assume created the observed data

  • observed data: e.g. sales
  • Parameters: e.g. demand model (for parametric estimation)
23
Q

Estimation objectives

A

unbiased
efficient
consistent

24
Q

Estimation objectives

unbiased

A
  • expected value of the estimator equals the actual value of the parameter
  • estimate is not systematically too high or too low
25
Q

Estimation objectives

Efficient

A
  • estimator is unbiased AND has as little variance as possible
  • Cramer-Rao bound provides a lower bound on the variance
26
Q

Estimation objectives

consistent

A
  • estimator converges to the true value as the sample size increases
  • increasing the number of observations provides better results
27
Q

Estimation challenges

A

Endogeneity
Constrained observations
Small number of observations
Biased data

28
Q

Estimation challenges

Endogeneity

A

explanatory variable is correlated with the error term

High prices lead to high demand?
Simultaneity: prices are driven by expected demand

29
Q

Estimation challenges

Constrained observations

A

Observations are systematically censored

There were never more than 100 bookings?
The capacity never exceeded 100 units!

30
Q

Estimation challenges

Small number of observations

A

Large samples more closely approximate the population

The previous three observations indicate an upward trend
- but can it be trusted?

31
Q

Estimation challenges

Biased data

A

The sample systematically differs from the population

Data from the loyalty program indicates a high rate of repeat bookings - but not for all customers!

32
Q

Minimum square error:

Linear regression

A
  • 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
33
Q

Regression Estimators are causal predictions

Advantages and disadvantages

A

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
34
Q

Regression Estimators for demand models: Variants

A
  • assuming different shapes of the regression function

- i.e. to predict demand from functions of price and product characteristics

35
Q

Regression Estimators for demand models: Variants

Kinds of variants

A

Probit

  • probability of one event
  • > such as buying or not buying

Multinomial logit/probit

  • set of discrete probabilities
  • > such as probabilistic product choice
36
Q

Censored or “constrained” demand

A
  • 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
37
Q

Censored or “constrained” demand

Simple unconstraining heuristic

A

If the product was not sold out:
- demand = sales

If the product was sold out
- demand = maximum(sales, previous forecast)

Related field: Survival analysis