2. Descriptive statistics in EViews

2. Descriptive statistics in EViews

Features of EViews:

• Data processing

(importing, editing, handling, exporting data)

• Basic statistical tools

(descriptive statistics, inference, graphical tools)

• Regression analysis

• Time series analysis

• Specification diagnostics, specification testing

2.1. Introduction to EViews

• EViews is based on objects Some typical EViews objects:

• Data series (single: series, collection of series: groups)

• graphs

• equations

How to enter EViews commands:

Basis of all EViews actions:

• workfile

Definition of a workfile:

• Container for all EViews objects with which you want to work (series, graphs, equations)

Features of a workfile:

• Prespecified data frequency

Creating an EViews-workfile:

• Either by typing the command create

• Or by clicking through the menu items File/New/ Workfile

−→ dialogue requesting two pieces of information: (1) Data frequency

Data frequency and data representation Frequency Representation annual 2014, 2015, etc. semi-annual 2015:1, 2015:2 quarterly 2015:1, ... , 2015:4 monthly 2015:01, ... , 2015:12 weekly mm/dd/yyyy, e.g. 03/26/2015

daily (5 days weeks) mm/dd/yyyy

daily (7 days weeks) mm/dd/yyyy

Generating data series:

• Manual data input

(invoking the EViews data editor by the command data)

• Importing data from external data bases (e.g. from Excel, Lotus, ...)

Afterwards, we may use data series

• to generate graphs

Two fundamental EViews concepts:

• Transformating data series (via the genr command)

• Setting the active sample (via the smpl command)

Objective of many data transformations:

Example:

Assume we are given the following series in EViews:

• EX RATE: the nominal Euro-USD exchange rate

• P EURO: the overall price level in Euroland

• P US: the overall price level in the US Creating the real exchange-rate series:

Some operators and functions for the genr command Operator Meaning Example

+ Sum

- Difference

* Product

/ Ratio

^ Power genr H = (A+B/(H+K))^2

log(x) Natural log genr Z = log(X) exp(x) Natural exp

abs(x) Absolute value

sqr(x) Square root

sin(x) Sine

Lagged values (lag operator, lags):

• Let P_t denote an overall price level at date t

• The inflation rate π_t between the dates t ₋1 and t is defined as

π_t = Pt − Pt−1 P_t−1

Lag operator in EViews:

• Let P be the price-level series in EViews

Setting the active sample:

• Sometimes, it may not be reasonable to consider all obser-vations of a series in statistical operations

• Via the smpl command we are able to restrict the data range to be processed

Example:

Assume that your worfile contains yearly GDP data between 1950 and 2015:

• If you only need to consider the time period 1970 until 2010, you set

smpl 1970 2010

Remarks:

• The smpl command allows us to further restrict our data base via the if statement

• If you only need to analyze the years between 1970 and 2010, in which the inflation rate exceeded 2%, you set

2.2. Descriptive statistics

Notation:

• Consider the data series x₁, . . . , x_T

• T is the number of observations, x_t is the t-th observation

Example:

Prices (in euros) of the mutual fund DEKALUX-JAPAN during the calender weeks #10 and #11 in 2002

Date t x_t x_(t) 03/04/2002 1 527.54 x₍₃₎ 03/05/2002 2 523.79 x₍₂₎ 03/06/2002 3 521.92 x₍₁₎ 03/07/2002 4 540.91 x₍₇₎ 03/08/2002 5 551.68 x₍₉₎ 03/11/2002 6 556.54 x₍₁₀₎ 03/12/2002 7 543.45 x₍₈₎ 03/13/2002 8 530.52 x₍₄₎ 03/14/2002 9 534.60 x₍₅₎

2.2.1. Histogram and empirical cumulative

distri-bution function

Definition 2.1: (Histogram)

The histogram divides the series range (the distance between the maximum and minimum values) into a number of equal length intervals (bins) and displays a count of the number of observa-tions that fall into each bin.

Definition 2.2: (Empirical cumulative distribution function)

Given the data series x₁, . . . , x_T, for every x _∈ R the empirical cumulative distribution function F_T : R _→ [0,1] is defined as

Histogram with descriptive statistics in EViews 0 1 2 3 520 525 530 535 540 545 550 555 560 Series: DEKALUX Sample 3/04/2002 3/15/2002 Observations 10 Mean 536.8990 Median 536.3200 Maximum 556.5400 Minimum 521.9200 Std. Dev. 11.51973 Skewness 0.340804 Kurtosis 2.018182 Jarque-Bera 0.595232 Probability 0.742587

Empirical cumulative distribution function in EViews 0.0 0.2 0.4 0.6 0.8 1.0 524 528 532 536 540 544 548 552 556 P robabi li ty DEKALUX

2.2.2. Measures of a single series

Minimum, maximum:

• Formulae: xmin = x₍₁₎, xmax = x_(T)

• EViews commands: =@min(DEKALUX), =@max(DEKALUX)

Arithmetic mean: • Formula: x = 1 T · (x1 + x2 + . . . + xT) = 1 T · T X t=1 x_t

Median: • Formula: xmed =    x_([T+1]/2) , if T odd 1 2 · h x_{(T /2)} + x_([T+2]/2)i , if T even

• EViews command: =@median(DEKALUX)

Variance, standard deviation:

• Formulae: s2 = 1 T ₋ 1· T X t=1 (x_{t −} x)2 , s = v u u u t 1 T ₋ 1 · T X t=1 (x_{t −} x)2

Skewness: • Formula: xskew = 1 T T X t=1   q₁ xt − x T P_T t=1 (xt − x)2    3

• EViews command: =@skew(DEKALUX)

Kurtosis: • Formula: xkurt = 1 T T X t=1   q₁ xt − x T P_T t=1(xt − x)2    4

2.2.3. Covariance and correlation

Now:

• Assume that you have collected pairwise observations (x₁, y₁), . . . ,(x_T, y_T) for the two data series X and Y in EViews

Covariance: • Formula: S_XY = 1 T ₋ 1 T X t=1 (x_{t −} x)(y_{t −} y)

Correlation coefficient: • Formula: R_XY = SXY S_{X ·} S_Y = P_T t=1(xt − x)(yt − y) rhP_T t=1(xt − x)2 i hP_T t=1(yt − y)2 i