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

• Forecasting, simulation studies

• Programming

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2.1. Introduction to EViews

Fundamental concept behind 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:

• Via the EViews menu (clicking)

• Via the command line (typing commands)

8

EViews screenshot

9

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

• Prespecified sampling period

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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

(2) Start date and end date

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Data frequency and data representation

Frequency Representationannual 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

integer date 1, ... , 150

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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

• in statistcial and econometric routines

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Two fundamental EViews concepts:

• Transformating data series(via the genr command)

• Setting the active sample(via the smpl command)

Objective of many data transformations:

• Creating new data series from existing data series

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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:

• genr EX RATE REAL = EX RATE * P US / P EURO

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Some operators and functions for the genr command

Operator Meaning Example+ Sum- Difference* Product/ Ratio^ Power genr H = (A+B/(H+K))^2log(x) Natural log genr Z = log(X)exp(x) Natural expabs(x) Absolute valuesqr(x) Square rootsin(x) Sinecos(x) Cosine genr Z = log(sqr(sin(Y)))

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Lagged values (lag operator, lags):

• Let Pt denote an overall price level at date t

• The inflation rate πt between the dates t−1 and t is definedas

πt =Pt − Pt−1

Pt−1

Lag operator in EViews:

• Let P be the price-level series in EViews

• The inflation rates may be generated via the command

genr INFL RATE = (P-P(-1))/P(-1)

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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 rangeto be processed

Example:

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

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

smpl 1970 2010

• Then, all subsequent EViews operations only process thesedata

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Remarks:

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

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

smpl 1970 2010 if INFL RATE > 2.0

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2.2. Descriptive statistics

Notation:

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

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

• The ordered series is x(1) ≤ x(2) ≤ . . . ≤ x(T )

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Example:

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

Date t xt 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)03/15/2002 10 538.04 x(6)

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2.2.1. Histogram and empirical cumulative distri-bution function

Definition 2.1: (Histogram)

The histogram divides the series range (the distance between themaximum and minimum values) into a number of equal lengthintervals (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, . . . , xT , for every x ∈ R the empiricalcumulative distribution function FT : R→ [0,1] is defined as

FT (x) =number of xt ≤ x

T.

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Histogram with descriptive statistics in EViews

23

0

1

2

3

520 525 530 535 540 545 550 555 560

Series: DEKALUXSample 3/04/2002 3/15/2002Observations 10

Mean 536.8990Median 536.3200Maximum 5 56.5400Minimum 5 21.9200Std. Dev. 11.51973Skewness 0.340804Kurtosis 2.018182

Jarque-Bera 0.595232Probability 0.742587

Empirical cumulative distribution function in EViews

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0.0

0.2

0.4

0.6

0.8

1.0

524 528 532 536 540 544 548 552 556

Pro

ba

bili

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 =1T· (x1 + x2 + . . . + xT ) =

1T·

T∑

t=1xt

• EViews command: =@mean(DEKALUX)

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Median:

• Formula: xmed =

x([T+1]/2) , if T odd12 ·

[

x(T/2) + x([T+2]/2)

]

, if T even

• EViews command: =@median(DEKALUX)

Variance, standard deviation:

• Formulae: s2 =1

T − 1·

T∑

t=1(xt − x)2 , s =

√

√

√

√

√

1T − 1

·T

∑

t=1(xt − x)2

• EViews commands: =@vars(DEKALUX), =@stdev(DEKALUX)

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Skewness:

• Formula: xskew =1T

T∑

t=1

xt − x√

1T

∑Tt=1 (xt − x)2

3

• EViews command: =@skew(DEKALUX)

Kurtosis:

• Formula: xkurt =1T

T∑

t=1

xt − x√

1T

∑Tt=1 (xt − x)2

4

• EViews command: =@kurt(DEKALUX)

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2.2.3. Covariance and correlation

Now:

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

Covariance:

• Formula: SXY =1

T − 1

T∑

t=1(xt − x)(yt − y)

• EViews command: =@covs(X,Y)

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Correlation coefficient:

• Formula: RXY =SXY

SX · SY=

∑Tt=1(xt − x)(yt − y)

√

[

∑Tt=1(xt − x)2

] [

∑Tt=1(yt − y)2

]

• EViews command: =@cor(X,Y)

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