Automatic Forecasting with R

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Presentation transcript:

Automatic Forecasting with R Andy Fisher andy@dfanalytics.com 12/31/2018 DF Analytics, Inc.

Agenda Forecasting in Supply Chain Management The R forecast package Additional considerations 12/31/2018 DF Analytics, Inc.

My Relevant Background Role in Professional Services at the SAS Institute as an Analytical Consultant focused on the implementation of SAS Forecast Server Role at Cisco Systems, first managing the application of SAS Forecast Server in supply chain consensus demand planning process, then as S&OP Manager, translating supply chain strategies into financial trade-offs 12/31/2018 DF Analytics, Inc.

Automatic Forecasting Explained Automatic forecasting relies on a computer to fit a proper set of models to every series and the computer picks the best one based on some sort of statistical test. Proper set of models is important. Proper is dependent on the demand patterns or time series properties An improper set of models can lead to lower forecast performance An improper statistic for model selection can lead to lower forecast performance Automatic forecasting is used in situations with more series than forecast analysts can typically handle Such as supply chain management 12/31/2018 DF Analytics, Inc.

Example: Forecast System in Supply Chain Planning Demand History Forecast System Demand Planning System Inventory Optimization Product level demand history provides input to forecasting system Statistical forecasting system provides baseline expectation of future demand Demand Planners demand plan with Stat forecast as baseline Expected sales not included in forecast are added by Demand Planners Once demand plan is finalized, component orders are determined through inventory optimization system In Supply Chain Management, a good forecast improves delivery times and reduces inventory holding cost 12/31/2018 DF Analytics, Inc.

Time Series Forecasting in R stats Relevant time series fitting functions in the Stats package arima: fit an ARIMA model to a univariate time series HoltWinters: computes Holt-Winters filtering of time series StructTS: fit a structural model for a time series by maximum likelihood lm: used to fit linear regression models Relevant forecasting functions in the Stats package predict.Arima: forecasts from models fitted by arima predict.HoltWinters: forecasts from models fitted by HoltWinters predict.StructTS: forecast from models fitted by StructTS predict.lm: predicted values based on linear object model 12/31/2018 DF Analytics, Inc.

Time Series Forecasting in forecast Package The R forecast package, authored by Rob Hyndman http://robjhyndman.com/software/forecast/ http://cran.r-project.org/web/packages/forecast/forecast.pdf Relevant fitting functions Arima: Fit ARIMA model to univariate time series (largely wrapper for stats package arima) auto.arima: Fit best ARIMA model to univariate time series ets: exponential smoothing state space model Croston: Forecasts for intermittent demand using Croston’s method Relevant forecasting functions forecast.Arima: Returns forecasts and other information for Arima and auto.arima fitted models forecast.ets: Returns forecasts and other information for univariate ets models forecast.StructTS: Returns forecasts and other information for univariate structural time series models 12/31/2018 DF Analytics, Inc.

auto.arima and ets Approach Automatically determine differencing needed for stationarity Then automatically estimate models using different AR and MA terms Forecast model is selected by AIC ets Based on the idea that exponential smoothing methods are optimal forecasts from innovations state space models The triplet (E,T,S) refers to 3 components: error, trend, seasonality ETS(M,Md,M) refers to a model with multiplicative errors, damped multiplicative trend, multiplicative seasonality Forecast model is selected by applying all relevant models, optimizing parameters, and selecting the best model by AIC auto.arima and ets algorithms explained in detail at: http://robjhyndman.com/papers/forecastpackage.pdf 12/31/2018 DF Analytics, Inc.

forecast Package auto.arima # load forecast package library(forecast) # forecast package ARIMA Inflationmodauto <- auto.arima(Inflationts) # view Inflationmodauto Inflationmodauto Series: Inflationts ARIMA(0,1,0) sigma^2 estimated as 3.188: log likelihood=-61.96 AIC=125.92 AICc=126.05 BIC=127.35 # forecast Inflationmodauto Inflationfcstauto <- forecast.Arima(Inflationmodauto, h=30) # view Inflationfcstauto Inflationfcstauto Point Forecast Lo 80 Hi 80 Lo 95 Hi 95 2012 2.565 0.2767618 4.853238 -0.9345584 6.064558 2013 2.565 -0.6710575 5.801058 -2.3841229 7.514123 2014 2.565 -1.3983449 6.528345 -3.4964129 8.626413 2015 2.565 -2.0114764 7.141476 -4.4341167 9.564117 12/31/2018 DF Analytics, Inc.

forecast Package ets Exponential Smoothing # load forecast package library(forecast) # forecast package ets Inflationets <- ets(Inflationts) # view Inflationets Inflationets ETS(M,Md,N) Call: ets(y = Inflationts) Smoothing parameters: alpha = 0.0051 beta = 0.0051 phi = 0.8762 Initial states: l = 14.2541 b = 0.7511 sigma: 0.4079 AIC AICc BIC 132.0158 134.3235 139.3445 # forecast ets forecastets <- forecast(Inflationets, h=30) 12/31/2018 DF Analytics, Inc.

auto.arima and ets Forecasts 12/31/2018 DF Analytics, Inc.

Other Relevant Features in forecast Package forecast package arima and exponential smoothing models can be manually specified, as well as automatically selected Accuracy: returns a set of accuracy summary measures of forecast accuracy ACF: auto-correlation function estimation seasonaldummy: returns matrices of seasonal dummies 12/31/2018 DF Analytics, Inc.

Additional Considerations Forecast package does not do automatic ARIMAX/transfer function specification This means lags for independent variables will need to be determined by hand See the ARIMAX model muddle, Rob Hyndman http://robjhyndman.com/researchtips/arimax/ Database for storage (RODBC, RMySQL, etc.) will be useful Some series perform better using hierarchical forecasting. Try hts package. For more flexible management of time series data, try zoo or xts package. 12/31/2018 DF Analytics, Inc.

Useful Resources An R Time Series Tutorial, R.H Shumway and D.S. Stoffer http://www.stat.pitt.edu/stoffer/tsa2/R_time_series_quick_fix.htm A Little Book of R for Time Series, Avril Coghlan http://a-little-book-of-r-for-time-series.readthedocs.org/en/latest/index.html R Data Import/Export, R Development Core Team http://cran.r-project.org/doc/manuals/R-data.pdf CRAN Task View: Time Series Analysis http://cran.r-project.org/web/views/TimeSeries.html CRAN Task View: Econometrics http://cran.r-project.org/web/views/Econometrics.html 12/31/2018 DF Analytics, Inc.