forecasting_lecture_03

forecasting_lecture_03 - Lecture Notes 3 1. Types of...

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1 Lecture Notes 3 1. Types of economic variables (i) Continuous variable – takes on a continuum in the sample space, such as all points on a line or all real numbers Example: GDP, Pollution concentration, etc. (ii) Discrete variables – finite number of elements or an infinitely countable number, such as all positive integers. Example: Number of workers, etc. (iii) Categorical data are grouped accordingly to some quality or attribute Example: Sex or type of automobile. 2. Review of statistics (i) Population – the total group set of elements of interest. Sample – a subset of the population. We usually collect samples because it is too costly to sample the entire population. Example – College students’ survey in Kazakhstan Population is all college students Probability – the relative frequency or occurrence of an event after repetitive trials or experiments. Probability lies between 0 and 1 All probabilities for all events have to sum to 1 Example: 60% chance of rain today Implies a 40% of no rain, summing to one or 100%
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2 (ii) Probability distribution functions (PDF) – a function that associates each value of a discrete random variable with the probability that this value will occur. Denoted as p(x) or f(x) Cumulative probability distribution function (CDF) - integral of a probability function Denoted by a capital letter, such as P(x) or F(x).     x dt t f x P If you sum over all probabilities, then it has to equal one.     1  dt t f x P The normal probability distribution is shown below
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(iii) Descriptive statistical measures – describe a sample or population. Measures of central tendencies Mean – calculated by ) x ( f x x i i where f(x) is the pdf and x is the random variable. This is also the expected value If every observation is equally likely, then i x n 1 x where n is the number of observations Median – the middle point or observation when the data are ordered from smallest to largest. Mode – the value, which occurs most often in a distribution. The peak of a distribution Use calculus to find maximum value Range – the difference between the largest value in the sample (the maximum) and the smallest value (the minimum), min max x x R Variance – is a measure of deviation from the mean, denoted by 2 Variance has a problem If the units are in $’s, then variance is $ 2 The n-1 is the sample variance Degrees of freedom (df) – the amount of information you have, i.e. the number of observations Since you estimated the variance, you lose one piece of
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forecasting_lecture_03 - Lecture Notes 3 1. Types of...

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