Ch. 1. Introduction STA 4852 PDF

Introduction A Model-Building Strategy Ch.1. Introduction STA 4852 Jongik Chung Department of Statistics & Data Science University of Central Flori...

Introduction A Model-Building Strategy Ch.1. Introduction STA 4852 Jongik Chung Department of Statistics & Data Science University of Central Florida Introduction A Model-Building Strategy Table of Contents 1 Introduction 2 A Model-Building Strategy Introduction A Model-Building Strategy Introduction Introduction A Model-Building Strategy Introduction Time series data Data obtained from observations collected sequentially over time Extremely common Business: weekly interest rates, daily closing stock prices, monthly price indices, yearly sales figures, etc. Meteorology: daily high and low temperatures, annual precipitation and drought indices, and hourly wind speeds Agriculture: annual figures for crop and livestock production, soil erosion, and export sales Biological sciences: electrical activity of the heart at millisecond intervals Ecology: abundance of an animal species Introduction A Model-Building Strategy Introduction Examples Annual rainfall in Los Angeles Considerable variation in rainfall amount over the years Low (1988), high (1883), and in-between in value Interest Whether or not consecutive years are related in some way Use one year’s rainfall value to help forecast next Introduction A Model-Building Strategy Introduction Examples (Cont’d.) Annual rainfall in Los Angeles (cont,d.) The scatterplot shows no trends Not that interesting time series Introduction A Model-Building Strategy Introduction Examples (Cont’d.) An industrial chemical process A color property from consecutive batches in the process Values that are neighbors in time tend to be similar in size Introduction A Model-Building Strategy Introduction Examples (Cont’d.) An industrial chemical process (cont,d.) A slight upward trend Not terribly strong; the correlation ≈ 0.6 Introduction A Model-Building Strategy Introduction Examples (Cont’d.) Annual abundance of Canadian hare Time series plot of the abundance over about 30 years Neighboring values are very closely related Introduction A Model-Building Strategy Introduction Examples (Cont’d.) Annual abundance of Canadian hare (cont,d.) An upward trend Introduction A Model-Building Strategy Introduction Examples (Cont’d.) Monthly average temperatures in Dubuque, Iowa The average monthly temperatures (in degrees Fahrenheit) Displays a very regular pattern (seasonality) Observations twelve months apart are related in some manner or another Models must accommodate this variation while preserving the similarities Introduction A Model-Building Strategy Introduction Examples (Cont’d.) Monthly oil filter sales Seasonality? January values tended to be related to other January values February values tended to be related to other February values, and so forth Introduction A Model-Building Strategy Introduction Examples (Cont’d.) Monthly oil filter sales (Cont’d.) Use plotting symbols Seasonality is much easier to see Plotting methods are useful for finding patterns Introduction A Model-Building Strategy A Model-Building Strategy Introduction A Model-Building Strategy A Model-Building Strategy Three main steps in model-building process 1 Model specification (or identification) The classes (groups) of time series models are selected that may be appropriate for a given observed series Check time series plot, compute statistics, apply prior knowledge of the subject matter in which the data arise The chosen model at this point is tentative Principle of parsimony: The simplest model that will adequately represent the time series Introduction A Model-Building Strategy A Model-Building Strategy Three main steps in model-building process (Cont’d.) 2 Model fitting Finding the best possible estimates of the unknown parameters within a given model Least squares Maximum likelihood 3 Model diagnostics Assessing the quality of the model goodness of fit, model assumptions Adequate → complete modeling; the model may be used to forecast future values Inadequate → return to step 1