Добавил:

Upload Опубликованный материал нарушает ваши авторские права? Сообщите нам.

Вуз:

Челябинский Государственный Университет

Предмет:

[НЕСОРТИРОВАННОЕ]

Файл:

Eviews5 / EViews5 / Docs / EViews 5 Command Ref.pdf

Скачиваний:

Добавлен:

23.03.2015

Размер:

5.23 Mб

Скачать

☆

<<< < Предыдущая 98 99 100 101 102 103 104 105 106 107 108 109110 / 145110 111 112 113 114 115 116 117 118 119 120 121 122 > Следующая >>>

		Descriptive Statistics—577


@pc(x)	one-period percentage change	equals @pch(x)*100
	(in percent)

@pch(x)	one-period percentage change	( X − X( −1) ) ⁄ X( −1 )
	(in decimal)

@pca(x)	one-period percentage	equals @pcha(x)*100
	change—annualized (in per-
	cent)

@pcha(x)	one-period percentage	@pcha(x)
	change—annualized (in deci-	@pcha(x)
	change—annualized (in deci-	= ( 1 + @pch( x) )n − 1
	mal)	= ( 1 + @pch( x) )n − 1
	mal)
		where n is the lag associated
		with one-year (n = 4 ) for
		quarterly data, etc.).

@pcy(x)	one-year percentage change (in	equals @pchy(x)*100
	percent)

@pchy(x)	one-year percentage change (in	( X − X( −n) ) ⁄ X( − n) , where
	decimal)	n is the lag associated with one-
		year ( n = 12 ) for annual data,
		etc.).

Descriptive Statistics

These functions compute descriptive statistics for a specified sample, excluding missing values if necessary. The default sample is the current workfile sample. If you are performing these computations on a series and placing the results into a series, you can specify a sample as the last argument of the descriptive statistic function, either as a string (in double quotes) or using the name of a sample object. For example:

series z = @mean(x, "1945m01 1979m12")

w = @var(y, s2)

where S2 is the name of a sample object and W and X are series. Note that you may not use a sample argument if the results are assigned into a matrix, vector, or scalar object. For example, the following assignment:

vector(2) a

series x

a(1) = @mean(x, "1945m01 1979m12")

578—Appendix D. Operator and Function Reference

is not valid since the target A(1) is a vector element. To perform this latter computation, you must explicitly set the global sample prior to performing the calculation performing the assignment:

smpl 1945:01 1979:12

a(1) = @mean(x)

To determine the number of observations available for a given series, use the @obs function. Note that where appropriate, EViews will perform casewise exclusion of data with missing values. For example, @cov(x,y) and @cor(x,y) will use only observations for which data on both X and Y are valid.

In the following table, arguments in square brackets [ ] are optional arguments:

•[s]: sample expression in double quotes or name of a sample object. The optional sample argument may only be used if the result is assigned to a series. For @quantile, you must provide the method option argument in order to include the optional sample argument.

If the desired sample expression contains the double quote character, it may be entered using the double quote as an escape character. Thus, if you wish to use the equivalent of,

smpl if name = "Smith"

in your @MEAN function, you should enter the sample condition as:

series y = @mean(x, "if name=""Smith""")

The pairs of double quotes in the sample expression are treated as a single double quote.

Function	Name	Description

@cor(x,y[,s])	correlation	the correlation between X and Y.

@cov(x,y[,s])	covariance	the covariance between X and Y.

@inner(x,y[,s])	inner product	the inner product of X and Y.

@obs(x[,s])	number of observa-	the number of non-missing obser-
	tions	vations for X in the current sam-
		ple.

@mean(x[,s])	mean	average of the values in X.

@median(x[,s])	median	computes the median of the X
		(uses the average of middle two
		observations if the number of
		observations is even).

@min(x[,s])	minimum	minimum of the values in X.

@max(x[,s])	maximum	maximum of the values in X.

		By-Group Statistics—579


@quantile(x,q[,m,s])	quantile	the q-th quantile of the series X. m
		is an optional integer argument for
		specifying the quantile method: 1
		(rankit - default), 2 (ordinary), 3
		(van der Waerden), 4 (Blom), 5
		(Tukey).

@stdev(x[,s])	standard deviation	square root of the unbiased sam-
		ple variance (sum-of-squared
		residuals divided by n − 1 ).

@sum(x[,s])	sum	the sum of X.

@sumsq(x[,s])	sum-of-squares	sum of the squares of X.

@var(x[,s])	variance	variance of the values in X (divi-
		sion by n ).

By-Group Statistics

The following “by group”-statistics are available in EViews. They may be used as part of a series expression statements to compute the statistic for subgroups, and to assign the value of the relevant statistic to each observation.

Function	Description

@obsby(arg1, arg2[, s])	Number of non-NA arg1 observations for each
	arg2 group.

@sumsby(arg1, arg2[, s])	Sum of arg1 observations for each arg2 group.

@meansby(arg1, arg2[, s])	Mean of arg1 observations for each arg2 group.

@minsby(arg1, arg2[, s])	Minimum value of arg1 observations for each
	arg2 group.

@maxsby(arg1, arg2[, s])	Maximum value of arg1 observations for each
	arg2 group.

@mediansby(arg1, arg2[, s]) Median of arg1 observations for each arg2
	group.

@varsby(arg1, arg2[, s])	Variance of arg1 observations for each arg2
	group.

@stdevsby(arg1, arg2[, s])	Standard deviation of arg1 observations for each
	arg2 group.

@sumsqsby(arg1, arg2[, s])	Sum of squares of arg1 observations for each
	arg2 group.

580—Appendix D. Operator and Function Reference

@quantilesby(arg1, arg2,	Quantiles of arg1 observations for each arg2
[, s])	group.

@skewsby(arg1, arg2[, s])	Skewness of arg1 observations for each arg2
	group.

@kurtsby(arg1, arg2[, s])	Kurtosis of arg1 observations for each arg2
	group.

@nasby(arg1, arg2[, s])	Number of arg1 NA values for each arg2 group.

With the exception of @QUANTILEBY, all of the functions take the form:

@STATBY(arg1, arg2[, s])

where @STATBY is one of the by-group function keyword names, arg1 is a series expression, arg2 is a numeric or alpha series expression identifying the subgroups, and s is an optional sample literal (a quoted sample expression) or a named sample. With the exception of @OBSBY, arg1 must be a numeric series.

By default, EViews will use the workfile sample when computing the descriptive statistics. You may provide the optional sample s as a literal (quoted) sample expression or a named sample.

The @QUANTILEBY function requires an additional argument for the quantile value that you wish to compute:

@QUANTILEBY(arg1, arg2, q[, s])

For example, to compute the first quartile, you should use the q value of .25.

There are two related functions of note, @GROUPID(arg[, smpl])

returns an integer indexing the group ID for each observation of the series or alpha expression arg, while:

@NGROUPS(arg[, smpl])

returns a scalar indicating the number of groups (distinct values) for the series or alpha expression arg.

Special Functions

EViews provides a number of special functions used in evaluating the properties of various statistical distributions or for returning special mathematical values such as Euler’s constant. For further details on special functions, see the extensive discussions in Temme (1996), Abramowitz and Stegun (1964), and Press, et al. (1992).

Special Functions—581

Function	Description

@beta(a,b)	beta integral (Euler integral of the second kind):

B( a, b) = ∫

a − 1

( 1 − t)

b − 1

Γ( a) Γ( b)

= -----------------------

Γ( a + b)

for a, b > 0 .

@betainc(x,a,b)

incomplete beta integral:

a − 1

( 1 − t)

b − 1

------------------∫

B( a, b)

for 0 ≤ x ≤ 1 and a, b > 0 .

@betaincder(x,a,b,s)

derivative of the incomplete beta integral:

evaluates the derivatives of the incomplete beta integral

B( x, a, b) , where s is an integer from 1 to 9 corre-

sponding to the desired derivative:

∂B

-------

∂x

∂a

∂b

1 2 3

∂2B

∂2B ∂2B

4 5 6

---------

-------------

------------

∂x2

∂x∂a ∂x∂b

7 8 9

∂2B

---------

------------

---------

∂a2

∂a∂b

∂b2

@betaincinv(p,a,b)

inverse of the incomplete beta integral: returns an x

satisfying:

∫

a − 1

( 1 − t)

b − 1

p = ------------------

( a, b)

for 0 ≤ p ≤ 1 and a, b > 0 .

@betalog(a,b)

natural logarithm of the beta integral:

log B( a, b) = log Γ( a) + log Γ( b) − log Γ( a + b ) .

@binom(n,x)

binomial coefficient:

= ------------------------

x!( n

− x)!

for n and x positive integers, 0 ≤ x ≤ n .

582—Appendix D. Operator and Function Reference

@binomlog(n,x)

natural logarithm of the binomial coefficient:

log ( n!) − log ( x!) − log ( ( n − x)!)

@cloglog(x)

complementary log-log function:

log ( − log ( 1 − x) )