Module 2

what is the ecological def of trend

what is the statistical def of trend

much more robust

def of period

then what is a seasonal component

after applying the double angle formula whats the generic equation for harmonic regression

what do 𝛾1 and 𝛾2 = and what do the control

seasonal trend

what do

• 𝛾

• p

• θ

  represent

applitude

period

possition

of the wave

• what is our primary interest

• what can obscure this

• so what do we do before analysing time series

• trend

• seasonality

• remove it

whats the generic form of a time series model

give the names of the two non parametric approaches for estimating trend

Mann Kendell and Seasonal Kendell test

when is Mann Kendal test usually used

short time series

environmental and climate data

trend isnt just linear, it flucuates but it is consistent in one direction

what are the 4 steps of the test

what is the equation for S

what are the hypothesis tests and what do you compare S to

equation for kendel rank coeff and what is D

What is the seasonal kendell test

what do we do to a time series to make sure our model doesnt have lots of parameters

smooth it

what are the three smoothing techniques

LoWESS

splines

addative models

how does LoWESS work

adv and dis of LoWESS

how do splines work

where do they join

whats the general equation

and the estimated f()

what is p and how does p influence our model

what does penalized splines do and why would we use penalized splines

we use them as picking p is hard

give me the

• general form of the addative model

• the form when trend and seasonality are independent

• and when they interact

what does edf tell you

how non linear a relationship is

what does a higher and lower edf mean

how do yoy compare models with a smooth term (m1) and a term not smoothed (m2)

anova(m2,m1)

if pvalue <0.05 prefer m1 (smooth term)

what is autocorrelation

correlation of a variable with itself over time

how does auto cor effect sample size, and how does this effect our results

smaller n

underestimate se, so narrow CI, so miss leading results

Whats does a Autocorrelation function do

estimates temporal dependence in a time series

ACF function at lag k

CI for ACF

what are the two options for accounting for auto cor in our model

• option one is to treat it as a nuisance (adjust the standard error)

• options two is model explicitly, either using harmonic regression of ARIMA

• difference between AR and MA

• and what are there equations

• and what are there parameters

• AR uses a function of pervious values

  MA is a function of previous set of error terms

• in book

• AR parameter and regression parameter

For change points how do you model a mean shift

indication function

equation in book

what is the model for a slope change

whats the approach for a more complex model in change points

change is gradual we use best cable model, giving a transition phase often using a smooth curve

whats the two step guild for unknown change points

what are the Gumbel, Frechet and, Weibull equations

what do an, bn and alpha represent

what is the generalised extreme value distribution

now what is the location, scale and slope parameters

give the rules for the slope parameter and how this links to the three other equations

what using R what order are the parameters shown

alphabetical

l - location

sc - scale

sl - slope

how do you assess the fit of the GEV dis

return level plot, if points along the line then good fit

whats an alternative approach at looking at extreme values when our data is perhaps irregular

peak over threshold

what is y

threshold excess y = x - u where x> u

what is the model of y

how do you choose a threshold

residual life plot, where area shows linearity

what is sometimes the issue with extreme values and how do you account for this

• they are correlated, so excedances aren’t independent

• model with ARIMA or decluster