If two variable Xt and yt are said to be cointegrated, which of the following statements are true?
1)Xt and Yt must both be stationary.
2) Only one linear combination of Xt and Xt will be stationary.
3)The cointegrating equation for X1 and Y1 describes the short run relationship between the two series.
4)The residuals of a regression of Y1 and X1 must be stationary.
a)2 and 4 only
b)1 and 3 only
c)1,2 and 3 only
d)1,2,3 and 4
Answers
Answer:
(B) 1 and 3 only
Explanation:
xt and yt must both be stationary
the cointegrating equation for x1 and y1 describes the short run relationship between the two series
Answer:
The answer is b) 1 and 3 only
Explanation:
In mathematics, a linear aggregate is an expression made out of a set of phrases by using multiplying each term via a consistent and adding the outcomes (e.g. a linear mixture of x and y might be any expression of the form ax + via, wherein a and b are constants).The concept of linear combinations is central to linear algebra and related fields of arithmetic. most of this newsletter offers with linear mixtures in the context of a vector space over a field, with some generalizations given at the end of the object.
permit V be a vector area over the field k. As typical, we call elements of V vectors and make contact with factors of k scalars. If v1,...,vn are vectors and a1,...,an are scalars, then the linear mixture of those vectors with those scalars as coefficients is there is some ambiguity within the use of the time period "linear combination" as to whether or not it refers back to the expression or to its fee.
In most instances the price is emphasised, as inside the announcement "the set of all linear combinations of v1,...,vn always paperwork a subspace". however, one may also say "two special linear mixtures can have the same value" in which case the reference is to the expression. The diffused distinction among these uses is the essence of the perception of linear dependence: a family F of vectors is linearly independent precisely if any linear combination of the vectors in F (as value) is uniquely so (as expression). anyhow, even when considered as expressions, all that matters approximately a linear aggregate is the coefficient of every vi; trivial adjustments consisting of permuting the terms or including phrases with 0 coefficient do no longer produce distinct linear combos.
In a given scenario, ok and V may be precise explicitly, or they will be obvious from context. if so, we regularly communicate of a linear combination of the vectors v1,...,vn, with the coefficients unspecified (besides that they should belong to okay). Or, if S is a subset of V, we can also communicate of a linear mixture of vectors in S, where each the coefficients and the vectors are unspecified, except that the vectors have to belong to the set S (and the coefficients must belong to okay). in the end, we may additionally talk truely of a linear aggregate, wherein nothing is certain (except that the vectors ought to belong to V and the coefficients must belong to okay); in this example one might be relating to the expression, since every vector in V is really the cost of some linear mixture.
Explain linear combination properly with examples.
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If two variable Xt and yt are said to be cointegrated, which of the following statements are true?
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