Autocorrelation
There are generally three types of data that are available for empirical analysis.
They are,
(1) Cross section,
(2) Time series, and
(3) Combination of cross section and time series, also known as pooled data.
In time series data, for the observations in data follow a natural ordering over
time so that successive observations are likely to exhibit inter-correlations,
especially if the time interval between successive observations is short, such as a
day, a week, or a month rather than a year. This situation is termed as the
autocorrelation. However, in cross-section studies, data are often collected on
the basis of a random sample of cross-sectional units, so that there is no prior
reason to believe that the error term pertaining to sample is correlated with the
error term of another sample. If by chance such a correlation is observed in cross-
sectional units, it is called spatial autocorrelation, that is, correlation in space
rather than over time.
The condition of no correlation between members of series of observation
ordered in time (as in time series data) or space as in cross-sectional data) is
known as the assumption of no autocorrelation. That is, Autocorrelation doesn't
exist in the disturbance u, if,
E(ui, uj) = 0, if i# j
Otherwise, if the disturbance terms of a dataset that are ordered in time or
space are correlated each other, the situation is generally termed as
autocorrelation. That is,
E(u₁, uj) # 0, if i#j
, The above figure shows some possible patterns of auto and no autocorrelation
From the Figure, Part (a) to Part (d) errors follow some systematic patterns.
Hence, there is autocorrelation. Bute Part (e) reveals no such patterns and hence
there is no autocorrelation.
Positive and negative autocorrelation
Autocorrelation can be positive or negative. The value of autocorrelation varies
from -1 (for perfectly negative autocorrelation) and 1 (for perfectly positive
autocorrelation). The value closer to 0 is referred to as no autocorrelation.
Positive autocorrelation occurs when an error of a given sign between two values
of time series lagged by k followed by an error of the same sign. When data
exhibiting positive autocorrelation is plotted, the points appear in a smooth snake-
like curve, Negative autocorrelation occurs when an error of a given sign between
two values of time series lagged by k followed by an error of the different sign.
With negative autocorrelation, the points form a zigzag pattern if connected
Reasons of Autocorrelation
The following are the major reasons for autocorrelation.
1. Inertia: - Silent feature of most of the time series is inertia or sluggishness.
Well known examples in time series are GNI, price Index.
2. Specification Bias: Excluded variable case: Residuals (which are estimate of
us) may suggest that same variable that were originally candidates but were not
included in the model for a variety of reasons should be included.
3. Specification bias : incorrect functional form
Use of incorrect functional form of regression analysis may also leads to the
problem of autocorrelation
4. Cobweb phenomenon
There are generally three types of data that are available for empirical analysis.
They are,
(1) Cross section,
(2) Time series, and
(3) Combination of cross section and time series, also known as pooled data.
In time series data, for the observations in data follow a natural ordering over
time so that successive observations are likely to exhibit inter-correlations,
especially if the time interval between successive observations is short, such as a
day, a week, or a month rather than a year. This situation is termed as the
autocorrelation. However, in cross-section studies, data are often collected on
the basis of a random sample of cross-sectional units, so that there is no prior
reason to believe that the error term pertaining to sample is correlated with the
error term of another sample. If by chance such a correlation is observed in cross-
sectional units, it is called spatial autocorrelation, that is, correlation in space
rather than over time.
The condition of no correlation between members of series of observation
ordered in time (as in time series data) or space as in cross-sectional data) is
known as the assumption of no autocorrelation. That is, Autocorrelation doesn't
exist in the disturbance u, if,
E(ui, uj) = 0, if i# j
Otherwise, if the disturbance terms of a dataset that are ordered in time or
space are correlated each other, the situation is generally termed as
autocorrelation. That is,
E(u₁, uj) # 0, if i#j
, The above figure shows some possible patterns of auto and no autocorrelation
From the Figure, Part (a) to Part (d) errors follow some systematic patterns.
Hence, there is autocorrelation. Bute Part (e) reveals no such patterns and hence
there is no autocorrelation.
Positive and negative autocorrelation
Autocorrelation can be positive or negative. The value of autocorrelation varies
from -1 (for perfectly negative autocorrelation) and 1 (for perfectly positive
autocorrelation). The value closer to 0 is referred to as no autocorrelation.
Positive autocorrelation occurs when an error of a given sign between two values
of time series lagged by k followed by an error of the same sign. When data
exhibiting positive autocorrelation is plotted, the points appear in a smooth snake-
like curve, Negative autocorrelation occurs when an error of a given sign between
two values of time series lagged by k followed by an error of the different sign.
With negative autocorrelation, the points form a zigzag pattern if connected
Reasons of Autocorrelation
The following are the major reasons for autocorrelation.
1. Inertia: - Silent feature of most of the time series is inertia or sluggishness.
Well known examples in time series are GNI, price Index.
2. Specification Bias: Excluded variable case: Residuals (which are estimate of
us) may suggest that same variable that were originally candidates but were not
included in the model for a variety of reasons should be included.
3. Specification bias : incorrect functional form
Use of incorrect functional form of regression analysis may also leads to the
problem of autocorrelation
4. Cobweb phenomenon
