QBA 775 Time series regression

Standard error: standard deviation divided by the square root of the sample size.

Exact relationship: y = mx + b
Probabilistic relationship: y-hat = b-sub-zero + b-sub-one*x

How to evaluate accuracy?
SSR: sum of squares regression. Sigma (x-hat - x-bar)^2
The bigger the SSR, the "better" the model.
SSE: sum of squares error/residual. Sigma (x - y-hat)^2
The bigger the SSAE, the "worse" the model.
SST: Sum of squares total. Sigma (y - y-bar)^2

Coefficient of determination: R^2 = SSR/SST
Bigger is better
Perfect prediction: R^2 = 1
No prediction: R^2 = 0

Standard error: S-sub-e = square root of (SSE/degrees of freedom)

Taken together, SSR, SSE, and SST tell us how far off our model is.

Is there a correlation at all?
t = (b-sub-one - B-sub-one) / S-sub-b-one

P value: < 0.05 reject null hypothesis (95%)

Time-Series regression:
y = value being evaluated
x = time interval

Time horizon series: y = trend*cycle*season

Immediate: x < 1 week
Short-term: 1 week < x < 3 months
Medium-term: 3 months < x < 2 years
Long-term: qualitative forecasting

First-order model (linear trend)
y-hat = b-sub-zero + b-sub-one*x

Confidence interval: x-bar = Z*S-sub-x-bar

Second-order model (non-linear)
y-hat = b-sub-zero + b-sub-one*t + b-sub-two*t^2

Third-order model (exponential)
y-hat = a*e^(b*t)