TODAY: programa das festas:

Deterministic trend

Stochastic trend

TSP: trend stationary process

DSP: difference stationary process

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ACF: autocorrelation function

PACF: partial autocorrelation function

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ADF test

KPSS test

Page 24 handouts

Stationary: everything ok

Problem: when series is non-stationary and specify what kind of trend we have in the series.

The non-stationarity is due to what?

1. Deterministic: we are able to find one and only one equation to represent it

2. Stochastic aka random: it can have different trends

When the trend is unique I can find an equation to define it.

Spurious regression: regression without sense.

Before estimating a regression I need to check stationarity and the kind of trend that I have in

my data.

Data file excel: TRENDS

deterministic trend

deterministic trend

I can regress one in terms of the other.

EVIEWS In general when we have non stat, before looking for a regression I need to transform the

series in a stationary one. How to detrend the series? Depends from the type of trend we

have: stochastic or deterministic. Two different processes: TSP or DSP.

TSP: trend stationary process Process to remove a trend when series has deterministic trend. How can I remove the trend

(detrend the series)? Regressing the series as a function of time (adjusting to the type of data:

linear, quadratic, etc.). Yt=f(t)

linear deterministic trend

*If quadratic trend: y1t c t t^2

intercept Slope

stationary series

DSP: difference stationary process Excel file: sheet stochastic trend

I can fit here a quadratic trend

but this is not the most correct process. I cannot find just one type of trend in this series

stochastic trend. Regressing by computing the differences between two consecutive

observations get a new series: stationary one.

Do I have DSP? Yes, if the trend is stochastic. How can I detrend the series (or remove the

trend)? By taking the difference! Yt: original series. I can compute the : Delta yt=yt-yt(-1)

named as 1st differences

0

200

400

600

800

1

57

3

11

45

17

17

22

89

28

61

34

33

40

05

45

77

51

49

57

21

62

93

68

65

Adj Close

Adj Close

Object>generate series> d_apple=d(adj_close)

mean constant and variance non constant. Take differences again to make the variance less

variable. I dont have a de-trended series yet because the variance is not constant yet.

1. Take the log to stabilize the variance and the differences of the log of the prices to

stabilize the mean: get a rate of change

Rt=ln(pt)-ln(pt-1)

The variance in thesecond case remaisn more constant than oin the 1st case.

Compute both: log-difference

transformations!

Diflog_apple=dlog(adj_close)

The variance became even more constant! (despite of the pikes)

If yt is DSP there is a stochastic trend and the series is non-stationary! We say that the

series has a unit root.

ADF (augmented Dickey-Fooler test) TEST Null: the series has a unit root: non stationary

Reject the null to have a stationary series

Open variable>view>unit root test:

reject null

non stat because stochastic trend

KPSS H0: no unit root stationary

H1:unit root: non stationary

.

see if todays price is related with

yesterdays one

non stat process

RW: is a non stationary process: yt=???yt-1+error_t, with ???=1