Learnings from Forecasting - Principles and Practice

www.otexts.org/fpp

Basic Modeling

Intro & simple theory

ForecastingForecast+Model

www.otexts.org/fpp

Code at: https://github.com/thiakx/Forecasting_DSSG

Adapted from the Forecasting: Principles and Practice book

Judgmental Forecasts Machine Generated Forecasts

Judgmental Forecasts

The Basics

Judgmental Forecasts - Principles

Set the forecasting task clearly and concisely

Implement a systematic approach: -Document and justify

-Systematically evaluate forecasts

Segregate forecasters and users

Judgmental Forecasts - How to

Delphi Method - Panel of experts

Ask the executives, staff, customers

Use a proxy (similar cases, best / worst case)

Nate Silver

Machine Generated Forecasts

The Basics

The Basics - Time Series Decomposition

12 month seasonal

trend

The Basics - Seasonality

The Basics - Seasonality + Trend

The Basics - Remainder / Random Error

The Basics - Seasonal sub-series plot

The Basics

The Basics - Time Series Decomposition

then re-seasonalize with thisTrain model with this

The Basics - Time Series Decomposition

then re-seasonalize with thisTrain model with this

The Basics - Time Series Decomposition

95% confidence

80% confidence

then re-seasonalize with thisTrain model with this

The Basics - Time Series Decomposition

then re-seasonalize with thisTrain model with this

Seasonal and Trend decomposition using Loess (STL) code

Córdoba

Using seasonal-trend decomposition based on loess (STL) to explore temporal patterns of pneumonic lesions in finishing

pigs slaughtered in England, 2005–2011

Córdoba

Using seasonal-trend decomposition based on loess (STL) to explore temporal patterns of pneumonic lesions in finishing

pigs slaughtered in England, 2005–2011

STL is suitable as the overall trend fluctuates a fair bit

Machine Generated Forecasts

Time Series Forecasting: Exponential smoothing

Time Series Forecasts - Holts-Winters

Time Series Forecasts - Exponential Smoothing

Time Series Forecasts - Exponential Smoothing

More relevantLess relevant

Something to represent fall in relevance?

Time Series Forecasts - Exponential Smoothing

Smoothing Parameter α = 0.8 0.80.160.0320.064

T1T2T3T4

T1-T4

Time Series Forecasts - Exponential Smoothing

T1-T4

Smoothing Parameter α = decided by minimizing error rate

Time Series Forecasts - Damping

Undamped projection

Damped projection

Time Series Forecasts - Additive vs Multiplicative

The additive method is preferred when the

seasonal variations are roughly constant

through the series, while the multiplicative method is preferred when the seasonal

variations are changing proportional to the level of the series.

Time Series Forecasts - Holts-Winters

Link to: Usage of Modified Holt-Winters Method in the Anomaly Detection of Network Traffic: Case Studies

Link to: Usage of Modified Holt-Winters Method in the Anomaly Detection of Network Traffic: Case Studies

Holt-Winter is suitable as the most recent behavior that deviates from norm is worth a lot more than past behavior

Machine Generated Forecasts

Time Series Forecasting: ARIMA Models

(AutoRegressive Integrated Moving Average)

Time Series Forecasts - ARIMA with Drift

ARIMA(3,1,1)(0,1,1)[12] with drift

Time Series Forecasts - ARIMA with Drift

ARIMA(3,1,1)(0,1,1)[12] with drift

Allow forecasts to change over time

Number of periods per season.

} }Non-

Seasonal Part

Seasonal Part

Time Series Forecasts - ARIMA with Drift

ARIMA(3,1,1)(0,1,1)[12] with drift

Allow forecasts to change over time

Number of periods per season.

p = order of the autoregressive part; d = degree of first differencing involved;

q = order of the moving average part.} }

Non- Seasonal

Part

Seasonal Part

}(p,d,q) }(p,d,q)

Time Series Forecasts - Auto Regression

In a multiple regression model, we forecast the variable of interest using a linear combination of predictors.

!vs !

In an autoregression model, we forecast the variable of interest using a linear combination of past values of the variable

(regression of the variable against itself)

Time Series Forecasts - Auto Regression

In a multiple regression model, we forecast the variable of interest using a linear combination of predictors.

!vs !

In an autoregression model, we forecast the variable of interest using a linear combination of past values of the variable

(regression of the variable against itself)

Order = no. of past values

Time Series Forecasts - Differencing

What we doing in (b) is differencing by computing the differences between consecutive observations.

The goal is to eliminate trend and seasonality.

(a) Dow Jones index (b) Daily change in Dow Jones index

Time Series Forecasts - Differencing

What we doing in (b) is differencing by computing the differences between consecutive observations.

(a) Dow Jones index (b) Daily change in Dow Jones index

Order = no. of difference needed

Time Series Forecasts - Moving Average

Rather than use past values of the forecast variable in a regression, a moving average model uses past forecast errors in a regression-like model (a weighted moving average of the past few forecast errors).

Time Series Forecasts - Moving Average

Rather than use past values of the forecast variable in a regression, a moving average model uses past forecast errors in a regression-like model (a weighted moving average of the past few forecast errors).

Order = no. of past values

Time Series Forecasts - ARIMA with Drift

ARIMA(3,1,1)(0,1,1)[12] with drift

Link to Seasonal ARIMA for Forecasting Air Pollution Index: A Case Study (Johor Malaysia)

Link to Seasonal ARIMA for Forecasting Air Pollution Index: A Case Study (Johor Malaysia)

ARIMA is one of the most popular time series forecasting methods. It is very flexible and can handle complex scenarios

Time Series Forecasts - Comparison of Accuracy

Time Series Forecasts - Comparison of Accuracy

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STLARIMA

Holt-Winters