Time Series Lecture 1 - Time Series Models for Business EPBA Time Series Lecture 1 1 Introduction 1 A time series is a set of observations denoted by xt

Time Series Lecture 1 - Time Series Models for Business...

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Time Series Models for Business EPBA Time Series Lecture 1
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1 Introduction 1. Introduction • A time series is a set of observations, denoted by x t , each one being recorded at a specific time t. Discrete Time Series: The set of times, T 0 , at which observations are made is a discrete set, T {0 ±1 ±2 } N t th t th t e.g., T 0 = {0, ±1, ±2, …}. Note that the set contains a finite or countably infinite number of elements. Continuous Time Series: The set of times, T0, at which observations are made is an interval or at which observations are made is an interval or union of intervals of the real line, e.g., T 0 = {t: 0 t 1}.
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A Formal Definition A time series model [ 1 ] for the observed data {x t }, is a specification for the joint distribution of a sequence of random variables {X t }, of which {x } is postulated to be a realization of which {x t } is postulated to be a realization. 1 [ ] The term time series is often used to mean both the data and the process, of which it is a realization.
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