M15 - Time Series Analysis Flashcards
Time series analysis
- … unit if observation
- …. points in time
Describes the …. change in y
Used for ….
- 1 unit if observation
- various points in time
Describes the temporal change in y
Used for forecasting
Portfolio mgmt:
…-French …-factor model
“Observation that … …. of … have tended to be … than the market
–> (I) small … (II) stocks with … price-to …. ratio
CAPM : capital … … mgmt
“Uses … variable to describe the … of a portfolio”
–> add those … factors to capm to reflect the portfolio’s …. to these ….
Portfolio mgmt:
FAMA-French 3-factor model
“Observation that 2 CLASSES of STOCKS have tended to be BETTER than the market
–> (I) small CAPS (II) stocks with LOW price-to BOOK ratio
CAPM : capital ASSET PRICING mgmt
“Uses ONE variable to describe the RETURNS of a portfolio”
–> add those 2 factors to capm to reflect the portfolio’s EXPOSURE to these FACTORS
quantitative forecasting models are based on ..
two methological subgroups:
…on a mathematical model
one or multiple time series
one series: time series extrapolation
one/ multiple: causal forecasting methods
Time series extrapolation
- classes of importance:
- These 3 classes … … on … data
- possible combinations
- autoregressive (AR) models
- integrated (I) models
- moving average (MA) models
- These 3 classes DEPENDING LINEARLY on PREVIOUS data
- autoregressive moving avergage (ARMA)
- autoregressive integrated moving average (ARIMA)
When are the time series models suitable?
suitable, if Xt can be modelled as a linear function of earlier values of Xt-1
time series extrapolation:
Gaussian White Noise
–> samples are regarded as a sequence of serially uncorrelated random variables with zero mean and finite variance;
at any point in time its totally random what you observe
time series extrapolation: Moving Average (MA)
earlier effect of Xt-1 and the error term still has an effect on Xt
–> the output variable depends linearly on the current and various past values of a stochastic term
time series extrapolation:
Random walk
zero of Xt is the value of Xt-1 plus error term
–> describes a path that consists of a succession of random steps
time series extrapolation:
Autoregressive
earlier point Xt-1 has an effect on Xt but to a reduced extent (beta)
–> the output variable depends linearly on its own previous values and on a stochastic term
Causal forecasting methods
- represents
- based on
- models
- a model is specified that represents the causal relationships between the variables
- based on time series data
single equation models or simultaneous models
Formulation of a model
- basic idea:
- additive time series equation:
- multiplikative time series equation:
- what are the components?
- basic idea: splitting the time series components into different components –> time series analysis decomposition
- Y = A + K + S + u
- Y = AKS*u
Y = variable to be forecasted;
systematic: A = trend component (long-term development of y), K = cyclical component, S = seasonal component (cyclical variations of y around a long-term trend
Whats the Durbin-watson statistics?
- expected values
is there autocorrelation in the residuals (prediction errors)?
- the expected value of d is large for large T’s,
…for perfect positive correlation: 0
…for complete uncorrelated terms: 2
…for perfect negative correlation: 4
T + k
T
k
T + k = forecast value for the period
T = end of observation period
k = number of observation points in the future
Name different time series models
- linear time series model
- non-linear time series models:
- -> square-root model
- -> logarithmic model
- -> multiplicative model
- -> power regression model
on what does forecasting depend?
depends on the quality, which depends on how well the model fits the data
