Quant Flashcards
Confidence Interval for a Predicted Y-Value
coefficient ± (critical t-value)(standard error of forecast)
t test for each variable
est. regression parameter/std
df = n-k-1
R square
coefficient of deterination
= RSS/ SST
regression sum of squares/ total sum of squares
=SST- SSE (sum of squared errors)
/ SST
=explained variation/ total variation
SEE standard error of estimate
= square root of mean squared error (MSE)
MSE = SSE / (N-K-1)
RSS sum of squares
MSR = RSS / K
F test all coefficients collectively
-one tail
= MSR regression mean square
/ mean squared error MSE
reject H0 IF F> Critical, at least one of the coefficients is significantly different than zero, at least one of the independent variables in the regression model makes a significant contribution to the explanation of the dependent variables.
conditional heteroskedasticity
residual variance related to level of independent variables
Std error are unreliable, but the slope coefficients are consistent and unbiased.
Use BP chi-square test
use white-corrected std errors
Serial correlation
residuals are correlated.
Type I errors but the slope coefficients are consistent and unbiased.
Durbin-watson test
use Hansen method to adjust standard error
Multicollinearity
Two or more independent variables are correlated.
Too many type iI errors and the slope coefficients are unreliable.
Drop one of the correlated variables.
Both multicollinearity and serial correlation biases the standard errors of the slope coefficients.
log-linear trend model
In(yt) = bo+b1(t)
best for data series that exhibits a trend or for which the residuals are correlated or predictable or the mean is non-constant.
AR model
dependent variable is regressed against previous values of itself.
is correct if the autocorrelation of residuals from the model are not statistically significant at any lag.
use t-test
if significant, model is incorrectly specified and a lagged variable at the indicated lag should be added.
covariance stationary
meet the following 3 conditions:
- constant and finite mean
- constant and finite variance
- constant and finite covariance with leading or lagged values
use Dickey-fuller test
if AR is not stationary, correct with 1st differencing.
if it is, the mean-reverting level must be defined, b1 must <1
mean reversion
b0/(1-b1)
value of the variable tends to fall when above its mean and rise when below its mean.
unit root
if the value of the lag coefficient = 1
the time series has a unit root and will follow a random walk process.
uniti root is not covariance stationary.
if it is unit root, value at t = value t-1 + a random error
mean reverting level is undefined
random walk
one for which the value in one period = value in another period + a random error
with a drift = xt = bo + xt-1 + error
without drift = xt-1 + error
1st differencing
to correct autoregressive model
subtract the value of the time series in the immediately preceding period from the current value of the time series to define a new variable
yt = xt - xt-1 (bo=b1=0)
covariance stationary
seasonality
tested by calculating autocorrelation of error terms.
to adjust for seasonality, an additional lag of the variable is added to the original model.
RMSE root mean squared error
used to assess the predictive accuracy autoregressive models
the lower the better
cointegration
2 time series are economically linked or follow the same trend and that relationship is not expected to change
the error term is covariance stationary and t-test is reliable.
test for unit root use DF test
if reject null hypothesis of a unit root, the error terms generated by the 2 times series are covariance stationary and the two series are coingegrated.
If both time series are covariance stationary, model is reliable.
If only the dependent variable time series or only the independent time series is covariance stationary, the model is not reliable.
If neither time series is covariance stationary, you need to check for cointegration.
ARCH autoregressive conditional heteroskedasticity
describes the condition where the variance of the residuals in one time period within a time series is dependent on the variance of the residuals in another period.
if true, std of regression coefficient in AR model and the hypothesis test of these coefficients are invalid.
use generalized least squares
supervised learning
a machine learning technique in which a machine is given labelled input and output data and models the output data based on the input data.
unsupervised learning
labeled data not provided, use unlabelled data that the algorithm uses to determine the structure of the data
a machine is given input data in which to identify patterns and relationships, but no output data to model.
deep learning algorithms
algorithms such as neural networks and reinforced learning learn from their prediction errors and are used for complex tasks such as image recognition and natural language processing.
technique to identify patterns of increasing complexity and may use supervised or unsupervised learning.
> 20 networks
have an agent seeking to max a defined reward given defined constrains.
overfitting
results from having a large # of independent variables, resulting in an overly complex model which may have generalized random noise that improves in-sample forecasting accuracy, but not for out-of sample.
use complexity reduction
- a penalty is imposed to exclude features that are not meaningfully contributing to out-of-sample prediction accuracy
and cross validation
