ECONOMETRICS INTRO (L0&L1) Flashcards
Descriptive statistics
Using mean,variance and correlation etc to help us understand the affect of variables
Forecasting
Predicting future outcomes eg interest rates
Estimating
How much one variable will affect another
Big data
How we analyse huge/complex data sets
Properties of big data
Volume
Variety
Velocity
Veracity
Volume
Large no of observations/variables
Variety
Different forms data comes in (video,text)
Velocity
How quick data can be recorded eg facebook posting
Veracity
The quality of the data
(A+B)’ (transposed)
A’+B’
(A’)’ (transposed)
A
(KA)’ (transposed)
KA’
(AB)’ (transposed)
B’A’
Square matrix
Rows=columns, can’t find the inverse for any other type
Symmetric matrix
Transposed=not transposed A’=A
Inverse matrix
A x A’ = I
BA=AB=I
If the matrix has an inverse it’s invertible/non-singular
(A-1)-1
A
(A’)-1
(A-1)’
(AB)-1
B-1A-1
(BA)-1
A-1B-1
((AB-1))’
(AB’)-1=(B’A’)-1=(A’)-1(B’)-1
|A’|
|A|
|AB|
|A|B|
|KA|
K^n |A|
Where n is the number of rows/columns
Collinearity
The rows and columns are the same so the determinant is 0
(12
12)
A is invertible when…
The determinant does not equal 0, also means the rank= number of rows
Orthogonal
Xi’xj=0
Rank(AB)
If the rank isn’t equal of matrix A or B, then use the lower rank
Tr(A’)
Tr(A)
Tr(A+B)
tr(A)+tr(B)
Tr(AB)
Tr(BA) if they’re square matrices (cyclicity of trace)
Tr(KA)
Ktr(A)
A is positive definite if
The quadratic is >0
A is positive semidefinite if
The quadratic is >_0
A is negative definite if
The quadratic is <0
A is negative semidefinite if
The quadratic is <_0
Symmetric matrix properties
Positive definite, non singular
Semidefinite if det(A) and tr(A) are positive If A has a positive determinate, then A^k will also be positive
Idempotent
A^2=A eg Identity matrix