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po - intercept (the place in which trend function crosses OY axis (vertical axis), or this is the average level of Y in t=0 (time unit number byO)
Pi - slope - the average change of Y in 1 time unit (in our case the average yearly change)
We estaimate trend parameter with OLS (Ordinary Least Sguares) method.
Linear trend sample (our time series) in the population: yf = b0 + blt + st yt - observed values of variable y t - time variable
b0 - estimator of p0: sample intercept
bx - estimator of px: sample slope (sometimes called trend coeficient)
et - residuals (reszty) or error term, observed values of random component ę (xi) £-(y hat) - theoretical value of a trend function (value calculated from the model)
There are two generał types of time series:
o Additive - Y = trend + seasonality + error o Multiplicative - Y = trend*seasonality*error
Generally we have 2 seasonai models:
1. Additive - Y=trend+seasonallty+random ness - lt's wehen diviations from the trend are of the same level no matter where we r on our time series.
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