Introduction

1. Introduction • A time series is an ordered sequence of observations. • The ordering of the observations is usually through time, but may also be taken through other dimensions such as space. • Time series analysis deal with relationship between observations that are separated by k units of time or space (lagged observations). • We are interested to know how the present depends upon the past. • Time series occur in a variety of fields. week 1

2. Examples • In agriculture, we observe annual crop production and prices. • In economics, we observe daily stock prices, weekly interest rates, monthly price indices, quarterly sales and yearly earnings. • In engineering, we observe sound, electric signals and voltage. • In meteorology, we observe hourly wind speed, daily temperature and annual rainfall. week 1

3. Type of Time Series Data • A time series that can be recorded continuously in time, is said to be continuous. For example, electrical signals and voltage. • A time series that is taken only at specific time intervals is said to be discrete. For example, interest rates, volume of sales etc. week 1

4. Objectives • Understanding and description of the generating mechanism. • Modeling and inference. • Forecasting and prediction. • Optimal control of a system. week 1

5. Important note • The basic nature of a time series is that its observations are dependent or correlated, and the order of the observations is therefore important. • Statistical procedures and techniques that rely on independence assumptions are no longer applicable. • The statistical methodology available for analyzing time series is referred to as time series analysis. week 1

6. Time versus Frequency Domain • Time series approach, which uses autocorrelation and partial autocorrelation functions to study the evolution of a time series through parametric models, is known as frequency domain analysis. • An alternative approach, which uses spectral functions to study the nonparametric decomposition of a time series into its different frequency components, is known as frequency domain analysis. week 1

7. Graphical Methods • The preliminary goal is to describe the overall (macro) structure of data and to identify memory type of time series. • There are two types of memories: (1) Short memory – immediate past gives some information about immediate future but less information about long-term future. (2) Long memory – past gives (potentially) more information about future (long term). Includes series with trends or cycles (seasonality). • A basic useful graphical tool is a Time Series Plot. We plot the data versus time. week 1