# Statistics for Decision Makers - 33.01 - Forecasting

From Training Material

- Title
- 33.01 - Forecasting
- Author
- Bernard Szlachta (NobleProg Ltd) bs@nobleprog.co.uk
- Footer
- www.NobleProg.co.uk
- Subfooter
- Training Courses Worldwide

## Contents

- 1 Economists。
- 2 What is Forecasting。
- 3 What forecast is not。
- 4 Two kind of Forecasting Models。
- 5 Cassandra。
- 6 Cassandra paradox 。
- 7 Business Point of View。
- 8 Chaos Theory 。
- 9 Lyapunov time。
- 10 What is a Model。
- 11 Models。
- 12 Some Concepts 。
- 13 What to forecast。
- 14 Simplest way of forecasting 。
- 15 Regression model。
- 16 Regression Assumptions 。
- 17 Types of Regression 。
- 18 Ordinary Least Square 。
- 19 Moving Average 。
- 20 Simple Moving Average (SMA) 。
- 21 Weighted Moving Average (WMA) 。
- 22 Exponential Smoothing 。
- 23 Forecast Error Measures。
- 24 Forecast Error Measures 。
- 25 Time Series 。
- 26 Forecasting Exercises - Sprite Sales 。
- 27 Forecasting ETS。
- 28 ARIMA (auto)。
- 29 Trend Analysis 。
- 30 Detrending and ensemble methods。
- 31 Judgemental Methods。
- 32 Combining Models。

## Economists。

There are two types of economists:

- those who don't know how to forecast interest rates
- and those who think they know how to forecast interest rates

## What is Forecasting。

- Forecasting is the process of making statements about events whose actual outcomes have not yet been observed.
- Usually related to estimation for some variable of interest at some specified future date
**Prediction**is a similar, but more general term

## What forecast is not。

- Target
- A description of where we think we are heading, based on current assumptions
- Plan
- A set of future actions designed to reach an objective
- Budget
- A sum of money allocated to an activity or action to which an organization has committed itself

## Two kind of Forecasting Models。

- Momentum Forecasting Models

- We can predict, but our action will not change the assumptions of the forecast
- Usually mathematical or statistical models
- E.g. solar activity

- Interventions Forecasting Models

- We try to asses the future in order to make decisions which in turn can usually prevent the forecast from happening
- Most of these forecasts are based on judgement
- There is feedback, i.e. the forecast itself changes the future (e.g. if you don’t change course, you will hit an iceberg)

## Cassandra。

## Cassandra paradox 。

Don't confuse the **Cassandra Paradox** with **Cassandra Syndrome**

- Had the Trojans not ignored Cassandra would her prediction have been correct?

Raise your hand if you think her prediction would have been correct?

## Business Point of View。

- Decision-making lead time
- The time between taking a decision to do something and the impact being manifested
- Forecast horizon
- The period of time in the future covered by a forecast

- Implications

If the Decision-making lead time is longer than Forecast horizon, do not bother forecasting

## Chaos Theory 。

- Deals with dynamical systems that are highly sensitive to initial conditions
- AKA
*the butterfly effect* - The system can be fully deterministic (as oppose to probabilistic), but can look random
- Managers should recognize the differences between probabilistic, deterministic and chaotic systems
- E.g. organization itself is considered chaotic

## Lyapunov time。

- The
**Lyapunov time**is the limit of the predictability of the system - Examples of the Lyapunov time (without rare events)
- Solar system: 50 million years
- Pluto's orbit: 20 million years
- Organization: from 1 day to hundreds of years
- Scrum Team: 1 day to 30 days
- Hydrodynamic chaotic oscillations: 2 seconds

## What is a Model。

- A model is a simplified representation of the world
- Complex models are not usually "better"

## Models。

- Mathematical

- E.g. Revenue = Volume * Price
- If we increase speed from 100km/hour to 200km/hour for the train, the travel time will be reduced by 50%

- Statistical

- Regression, Neural Networks, etc...
- People who study 30 mins more per day, with a 95% confidence level, achieve around 20% better results on average

- Judgemental (gut feeling)

- E.g. "I think the recession will last 2 years longer"
- E.g. "Inflation will be around 2% next year"

## Some Concepts 。

### Risk and Uncertainty

- Risk
- Any deviation from a central forecast where the probability of occurrence can be estimated with a degree of confidence
- Uncertainty
- Any possible deviation from a central forecast where the probability of occurrence cannot be estimated with a degree of confidence

### Central vs Range Forecast

- Central forecast
- The "single point" forecast
- Range forecast
- The estimated range of possible outcomes

## What to forecast。

## Simplest way of forecasting 。

- Important Assumption
- The future will look like the past (no discontinuity happened!)

- Simple mean forecast

- The next customer will spend around £2000 (mean of previous purchases per customer)
- Usually a very big error of forecast (proportional to variance)

- Naive forecast

- Very low error (e.g. stock exchange prices)
- The exchange rate of USD/GBP will be as it was yesterday

## Regression model。

A relationship between a dependent variable and one or more independent variables.

E(Y | X) = f(X, β)

- The unknown parameters are denoted as β; this may be a scalar or a vector
- The independent variables, X
- AKA: covariate, explanatory, predictor, control variable
- The dependent variable, Y

## Regression Assumptions 。

- The sample is representative of the population for the inference prediction
- The error is a random variable with a mean of zero conditional on the explanatory variables
- The independent variables are measured with no error
- The predictors are linearly independent, i.e. it is not possible to express any predictor as a linear combination of the others. See Multicollinearity.
- The errors are uncorrelated
- The variance of the error is constant across observations (
**homoscedasticity**) - If not, weighted least squares or other methods might instead be used

## Types of Regression 。

- Shape of the function

- Linear
- Non-linear

- Number of predictors

- Simple (one predictor)
- General Multiple Regression

## Ordinary Least Square 。

- Finds the line which minimizes squared distance scores from the line
- Uses calculus

## Moving Average 。

The moving average is the plot line connecting all the (fixed) averages

- The moving average smooths the price data to form a trend following the indicators
- They do not predict the price direction, but rather define the current direction with a lag

- Types

- Simple Moving Average (SMA)
- Exponential Moving Average (EMA)

## Simple Moving Average (SMA) 。

## Weighted Moving Average (WMA) 。

## Exponential Smoothing 。

## Forecast Error Measures。

## Forecast Error Measures 。

## Time Series 。

- The data consist of a systematic pattern (usually a set of identifiable components) and random noise (error)
- Can be described in terms of two basic classes of components: trend and seasonality

## Forecasting Exercises - Sprite Sales 。

### Code to paste

```
sp = scan("Z:/sprite.dat")
plot(sp,type="l")
spts = ts(sp,start=1991,frequency=12)
par(tck=1,lab=c(20,5,14),col="red")
plot(spts)
```

## Forecasting ETS。

```
fc = forecast(spts)
print(fc)
plot(fc)
plot(fc$residuals)
lines(fc$fitted)
```

What are the sales of Sprite in Jan 1997 going to be? (Give range and point estimation)

## ARIMA (auto)。

```
ar = auto.arima(spts)
fc = forecast(ar)
plot(fc)
```

## Trend Analysis 。

- Smoothing involves some form of local averaging of data such that the nonsystematic components of individual observations cancel each other out
- The most common technique is moving average (mean or median)
- Fitting a function (usually linear)

## Detrending and ensemble methods。

More: R - Time Series

## Judgemental Methods。

- Surveys
- Delphi method
- Scenario building
- Technology forecasting
- Forecast by analogy

## Combining Models。

- Usually we use all models (Judgemental + Statistical + Mathematical)
- For example, if we want to predict the revenue, we have price and volume
- Price * volume (mathematical model)
- Finding trends and analysis of seasonality (statistical)
- Scenario for growth - trend slope = 0, slope = 0.2, slope = 0.5
- Multiple models can be used and compared which delivers the best results (smallest error or prediction), it is referred to as
**an ensemble model**