class: title-slide, center, middle # Methods of Empirical Finance ## Seminar (UE) ### Christoph Huber ### University of Innsbruck #### Master in Banking and Finance ### Winter term 2019/20 (this version: 2019-12-10) --- class: center, middle, inverse # Time Series Analysis ### Methods of Empirical Finance --- <footer></footer> # Time Series Analysis ### Time Series Processes > A time series `\(\{y_t\}\)` is an ordered set of (random) variables, where the (time) ordering is important. > Data obtained from observations collected _sequentially_ over time. .smaller[ .center[ <img 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" width="576" /> ] ] .smaller[ __Notation:__ Observations `\(y_t\)`, at time `\(t = 1, ..., T\)`. __Goals:__ _Explanation_ (understand or model the stochastic mechanism underlying the series) and _Prediction_ (Forecast future values) ] --- <footer></footer> # Time Series Analysis ### Univariate and Multivariate Time Series Analysis .smaller[ - time series analysis accounts for the fact that data points taken over time may have an _internal structure_ that could be utilized to draw conclusions about the series’ movements and to make predictions about its future path - the aim of time series analysis is to find an appropriate statistical model for the data and to use this model for prediction: in this way, _the variables are allowed to speak for themselves_, without the "confines" of economic theory <br> - __univariate time series models__ are a class of specifications to model and predict variables using only information contained _in their own past values_ (and possibly current and past values of an error term) - __structural models__, on the other hand, are multivariate in nature, and attempt to explain changes in a variable by reference to the movements in the current or past values of other (explanatory) variables (e.g., vector auto-regressive models, VAR) <br> - `\(\rightarrow\)` time series analyses can be applied to get knowledge about the underlying _data generating process_, to __estimate inherent patterns__ like trends, seasonality, or cyclical components, and to test economic hypotheses ] --- <footer></footer> # Time Series Analysis .center[ <img src="data:image/png;base64,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" width="504" /> ] --- <footer></footer> # Time Series Analysis ### Time Series Operators - the `\(i^{th}\)` __difference operator__ is defined by .center[ `\(\Delta_i y_t = y_t - y_{t-i}\)` ] -- <br> Examples: - first difference operator: `\(\Delta y_t = y_t - y_{t-1}\)` - second difference operator: `\(\Delta y_t = y_t - y_{t-2}\)` - Seasonal differencing, e.g.: `\(\Delta y_t = y_t - y_{t-12}\)` <br> In R: `diff()` --- <footer></footer> # Time Series Analysis ### Time Series Operators - the __lag operator__ is defined as .center[ `\(Ly_t = y_{t-1}\)` ] -- <br> - more generally: `\(L^{k} y_t = y_{t-k}\)` - thus, `\(y_t + \alpha_1 y_{t-1} + \alpha_2 y_{t-2} = (1 + \alpha_1 L + \alpha_2 L^2) y_t\)` <br> In R: `lag()` --- <footer></footer> # Time Series Analysis ### Mean and Variance of Time Series - time series may have both __stochastic__ and __deterministic__ components, e.g., a series with a deterministic trend and a stochastic white noise component: .center[ `\(y_t = \alpha + \beta t + \varepsilon_t \hspace{2em} \text{where } \varepsilon_t \sim i.i.d(0, \sigma^2)\)` ] -- - most time series models of financial markets will have a stochastic component, and so the __unconditional expectation__ and variance of the `\(t^{th}\)` observation on the time series can be calculated; for example in the model above .center[ `\(\mu_{y_t} = E[y_t] = E[\alpha + \beta t + \varepsilon_t] = \alpha + \beta t\)` <br> `\(\lambda_0 = Var[y_t] = E[(y_t - E[y_t])^2] = E[(\alpha + \beta t + \varepsilon_t - \alpha + \beta t)^2] = E[\varepsilon_t^2] = \sigma^2\)` ] --- <footer></footer> # Time Series Analysis ### Autocovariance and Autocorrelation of Time Series - the `\(s^{th}\)`__-order autocovariance__ of some time series `\(\{y_t\}\)`, i.e., the unconditional covariance of `\(y_t\)` and `\(y_{t−s}\)` (that is, the unconditional covariance _at lag s_ is .center[ `\(\lambda_s = Cov[y_t, y_{t-s}] = E[(y_t - E[y_t])(y_{t-s} - E[y_{t-s}])]\)` ] -- - for instance, for the series above, the `\(s^{th}\)`-order autocovariance is .center[ `\(\lambda_s = Cov[y_t, y_{t-s}] = E[(\alpha + \beta t + \varepsilon_t - \alpha + \beta t)(\alpha + \beta t + \varepsilon_{t-s} - \alpha + \beta t)]\)` `\(= E[\varepsilon_t \varepsilon_{t-s}] = 0\)` ] -- <br> - the __autocorrelation function__ is then defined by .center[ `\(\rho_s = Corr[y_t, y_{t-s}] = \frac{\lambda_s}{\lambda_0}\)` ] --- <footer></footer> # Time Series Analysis ### Autocovariance and Autocorrelation of Time Series - the __partial autocorrelation function__ between `\(y_t\)` and `\(y_{t-s}\)` is is the correlation between `\(y_t\)` minus the part explained by intervening lags and `\(y_{t-s}\)` (where `\(E^*\)` is the minimum mean-squared error prediction of `\(y_t\)` by `\(y_{t-1}, ..., y_{t-s+1}\)`) .center[ `\(\rho_s^* = Corr[y_t - E^*[y_t | y_{t-1}, ..., y_{t-s+1}], y_{t-s}]\)` ] - thus, the partial autocorrelation gives the partial correlation of a time series eith its own lagged values, controlling for intervening effects of values at shorter lags --- <footer></footer> # Time Series Analysis ### Returns in Financial Analysis and Modeling .smaller[ - Starting point is often __prices__, however, most often it is preferable to work with _returns_, i.e., prices have to be converted to returns <br> ] -- ### Arithmetic and logarithmic returns .smaller[ - let `\(p_t\)` denote the price at time `\(t\)`; the simple "arithmetic" return `\(R_t\)` and the _continuously compounded_ logarithmic return `\(r_t\)` are then defined by .center[ `\(R_t = \frac{p_t - p_{t-1}}{p_{t-1}} \hspace{3em} r_t = ln\left(\frac{p_t}{p_{t-1}}\right)\)` ] - arithmetic returns are _not symmetric_: e.g. an increase by 50% and a decrease by 50% lead to a total change of -25% - log returns (continuously compounded returns) are _time-additive_ but not additive across portfolios ] --- class:middle <footer></footer> # Stationarity --- <footer></footer> # Stationarity ### Weak Stationarity > A time series process `\(\{y_t\}\)` is said to be covariance stationary or > weakly stationary of the following requirements are satisfied: > 1. `\(E[y_t] = \mu\)` > 2. `\(Var[y_t] = \lambda_0^2 < \infty\)` > 3. `\(Cov[y_t, y_{t-s}] = \lambda_{t, t-s} \forall t, t-s\)` .smaller[ That is, a time series process is _weakly stationary_ if `\(...\)` - the mean is constant (independent of `\(t\)`), - the variance is a finite, positive constant, independent of `\(t\)`, and - the auto-covariance is a finite function of the lag `\(s\)`, but not of the absolute location of either observation on the time scale ] --- <footer></footer> # Stationarity ### Strong Stationarity > A time series process `\(\{y_t\}\)` is said to be strictly stationary or > strongly stationary if the joint probability distribution of any set of `\(k\)` > observations in the sequence `\(\{y_t, y_{t+1}, ..., y_{t+k}\}\)` is the same > regardless of the origin `\(t\)` in the time scale. .smaller[ That is, a time series process is said to be _strongly stationary_ if the joint probability distribution does not change when shifted in time, i.e., if for any `\(t_1, t_2, ..., t_T \in \mathbb{Z}\)`, any `\(k \in \mathbb{Z}\)`, and `\(T = 1, 2, ..., T\)`, `\(...\)` .center[ `\(F_{y_{t_1}, y_{t_2}, ..., y_{t_T}}(y_1, ..., y_T) = F_{y_{t_{1+k}}, y_{t_{2+k}}, ..., y_{t_{T+k}}}(y_1, ..., y_T)\)` ] I.e., a series `\(\{y_t\}\)` is strictly stationary if the distribution of its values remains the same is time progresses, implying that the probability that `\(y\)` falls within a particular interval is the same now as at any time in the past or future. ] --- <footer></footer> # Stationarity ### Financial Time Series In applications of time series analysis to financial markets, _return data_ and _price data_ have to be treated differently as we have to distinguish between __stationary__ and __non-stationary time series__: - __returns__ are mainly _stationary_ (mean-reverting, little autocorrelation) - __prices__ are mainly _non-stationary_ (time-trending, autocorrelation) <br> .smaller[ Note that some concepts – in terms of financial economics – such as, for instance, the volatility of time series or the correlation between two different processes, which apply to stationary processes, do not apply to non-stationary processes. ] --- <footer></footer> # Stationarity ### Example: Download stock price data ```r library(tidyverse) library(tidyquant) apple <- tq_get("AAPL") # download Apple Inc. (AAPL) prices ``` <br> .smaller[ Stata: `getsymbols` command (install using `ssc install getsymbols`) ] --- <footer></footer> # Stationarity ### Example: Apple Inc. stock price — a non-stationary time series .smaller[ ```r plot(zoo(apple$adjusted, apple$date)) ``` <img src="data:image/png;base64,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" width="540" /> ] --- <footer></footer> # Stationarity ### Example: Apple Inc. stock return — a stationary time series .smaller[ ```r apple <- apple %>% tq_mutate(select = adjusted, mutate_fun = periodReturn, period = "daily", type = "log") plot(zoo(apple$daily.returns, apple$date)) ``` <img src="data:image/png;base64,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" width="540" /> ] --- <footer></footer> # Stationarity ### Mean Reversion - stationary series exhibit a well-know property referred to as __mean-reversion__: due to its finite variance, a stationary process can never drift too far from its mean - the speed of mean reversion is determined by the _autocovariance_: mean reversion is quick when autocovariances are small and slow when autocovariances are large <br> -- - in finance, mean reversion refers to the assumption that security prices tend to move towards the average price over time: assets seem to be attractive to buy when the current price is below the average price and vice versa - in this sense, mean reversion is opposed by the empirically observed tendency for rising asset prices to rise further and falling prices to keep falling (__momentum__) --- <footer></footer> # Stationarity ### Stationarity vs. Non-Stationarity - any series with a trend in the mean will not be stationary: when prices appear to be trending, this is normally due to a stochastic rather than a deterministic trend - while prices (or log prices) in most markets are non-stationary, the first difference in prices – or, more usually, the __first difference in log prices__ (as these are approx. equal to returns) – are modeled as a stationary process --- <footer></footer> # Stationarity ### Integrated Processes > Let `\(\{y_t\}\)` be a non-stationary process such that `\(\Delta^d\{y_t\}\)` is stationary but > `\(\Delta^{d-1}\{y_t\}\)` is non-stationary. Then `\(\{y_t\}\)` is called integrated of order `\(d\)`, denoted `\(y_t \sim I(d)\)`. <br> __Example:__ - consider the time series process `\(y_t = \mu + y_{t-1} + u_t\)` where `\(u_t \sim WN(0, \sigma^2)\)` (referred to as _random walk with drift_); taking first difference of `\(y_t\)` yields `\(\Delta y_t = y_t - y_{t-1} = \mu + u_t\)`, i.e., the white noise error term which is stationary - i.e., a random walk is non-stationary but becomes stationary when taking the first difference; thus, a random walk is an _integrated process of order 1_, denoted `\(I(1)\)` --- <footer></footer> # Stationarity ### Tests for Stationarity: unit root tests A number of different statistical tests are available to test whether a time series is _stationary_ or _non-stationary_: _(augmented) Dickey-Fuller (GLS) test, Phillips-Perron test, KPPS test_, etc. - `\(H_0\)`: the (time series) process has a unit root, i.e., is _non-stationary_ - `\(H_1\)`: depending on test, usually _stationarity_ or _trend-stationarity_ of the time series --- <footer></footer> # Stationarity ### Tests for Stationarity: unit root tests .smaller[ ```r library(tseries) adf.test(apple$adjusted) ``` ``` ## ## Augmented Dickey-Fuller Test ## ## data: apple$adjusted ## Dickey-Fuller = -1.2799, Lag order = 14, p-value = 0.8832 ## alternative hypothesis: stationary ``` ```r pp.test(apple$adjusted) ``` ``` ## ## Phillips-Perron Unit Root Test ## ## data: apple$adjusted ## Dickey-Fuller Z(alpha) = -4.2365, Truncation lag parameter = 9, ## p-value = 0.8734 ## alternative hypothesis: stationary ``` ] --- <footer></footer> # Stationarity ### Tests for Stationarity: unit root tests .smaller[ ```r adf.test(apple$daily.returns) ``` ``` ## ## Augmented Dickey-Fuller Test ## ## data: apple$daily.returns ## Dickey-Fuller = -13.693, Lag order = 14, p-value = 0.01 ## alternative hypothesis: stationary ``` ```r adf.test(diff(log(apple$adjusted))) ``` ``` ## ## Augmented Dickey-Fuller Test ## ## data: diff(log(apple$adjusted)) ## Dickey-Fuller = -13.669, Lag order = 14, p-value = 0.01 ## alternative hypothesis: stationary ``` ] --- <footer></footer> # Stationarity ### Detrending Financial Time Series - since a trending time series is typically non-stationary, we would like to remove trends in order to make it a stationary time series (referred to as detrending) - importantly, trends might either be deterministic or stochastic in nature <br> - to remove a deterministic trend... ... compute deviations from a fitted line - to remove a stochastic trend... ... integrate the process, i.e., take differences --- <footer></footer> # Stationarity ### Detrending Financial Time Series .smaller[ .pull-left[ ```r plot(apple$date, apple$adjusted, type="l") abline(lm(adjusted ~ date, data = apple), col=2) ``` <img src="data:image/png;base64,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" width="576" /> ```r # # ``` ] .pull-right[ ```r apple$trend <- predict(lm(adjusted ~ date, data = apple)) apple$deviation <- apple$adjusted - apple$trend plot(apple$date, apple$daily.returns, type = "l", col = "darkgray") lines(apple$date, apple$deviation/400, col = 2) ``` <img src="data:image/png;base64,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" width="576" /> ] ] --- class: middle <footer></footer> # Autoregressive and Moving Average Models --- <footer></footer> # Autoregressive Processes, AR(p) - let `\(u_t\)` be a white noise process with `\(E[u_t] = 0\)` and `\(Var[u_t] = \sigma^2\)`, then an __autoregressive model of order__ `\(p\)`, denoted as `\(AR(p)\)`, is defined as .center[ `\(y_t = \alpha_0 + \alpha_1 y_{t-1} + ... + \alpha_p y_{t-p} + u_t\)` ] <br> - i.e., an autoregressive model is a process where the current value of `\(y\)` depends only on the value of `\(y\)` in previous periods plus an error term --- <footer></footer> # Autoregressive Processes, AR(p) .center[ <img src="data:image/png;base64,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" width="648" /> ] --- <footer></footer> # Autoregressive Processes, AR(p) .pull-left[ <img src="data:image/png;base64,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" 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" width="576" /> ] --- <footer></footer> # Moving Average Processes, MA(q) - let `\(u_t\)` be a white noise process with `\(E[u_t] = 0\)` and `\(Var[u_t] = \sigma^2\)`, then a `\(q^{th}\)` __order moving average processes__, denoted as `\(MA(q)\)`, is defined by .center[ `\(y_t = \mu + u_t + \theta_1 u_{t-1} + \theta_2 u_{t-1} + ... + \theta_q u_{t-q}\)` ] <br> - i.e., a moving average model is simply a linear combination of white noise processes, such that `\(y_t\)` depends on the current and previous values of a white noise disturbance term --- <footer></footer> # Moving Average Processes, MA(q) .center[ <img src="data:image/png;base64,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" width="648" /> ] --- <footer></footer> # Moving Average Processes, MA(q) .pull-left[ <img src="data:image/png;base64,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" 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" width="576" /> ] --- <footer></footer> # Autoregressive Moving Average Models (ARMA) - autoregressive moving average models (ARMA) provide a parsimonious description of a weakly stationary stochastic process in terms of two polynomials, one for the autoregression and one for the moving average - i.e., combining an AR(p) and a MA(q) model results in the __ARMA(p,q)__ model .centering[ `\(y_t = \alpha_0 + \alpha1 y_{t-1} + ... + \alpha_p y_{t-q} + u_t + \theta_1 u_{t-1} + ... + \theta_q u_{t-q}\)` ] <br> .smaller[ __Note:__ if the data shows evidence of non-stationarity, the ARIMA generalization (autoregressive integrated moving average models) might be applied in order to eliminate non-stationarity by an initial differencing step ] --- <footer></footer> # Autoregressive Moving Average Models (ARMA) .center[ <img src="data:image/png;base64,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" width="648" /> ] --- class: middle <footer></footer> # Model Identification --- <footer></footer> # Model Identification - the most crucial step in time series analysis is to identify and build a model based on the available data — i.e., to identify a process which best explains the observed movements over time <br> -- - the aim is to identify a process that leaves the residuals not being different from a white noise process (i.e., no exploitable information is contained in residuals) - in order to statistically examine whether a process is significantly different from white noise, several tests are available (e.g., _portmanteau Q test_, _Bartlett’s test_, _Box-Pierce test_, or _Ljung-Box test_) --- <footer></footer> # Model Identification ### Box-Jenkins Approach for Modelling Stochastic Processes __1. stationarity, model specification:__ check whether the series is stationary, determine the order `\((p, q)\)` of the model, apply graphical methods and (partial) autocorrelation function __2. estimation:__ estimate the parameters using non-linear least squares or maximum likelihood (ordinary least squares will be biased and/or inefficient) __3. diagnosis, model quality:__ examine residuals and check the model quality (information criteria) <br> .smaller[ Aim: establish a model as parsimonious as possible because the variance of the estimates is inverse proportional to the number of degrees of freedom, i.e., parameters in the model to be estimated ] --- <footer></footer> # Model Identification ### ACF and PACF | process | autocorrelation `\(\rho\)` | partial autocorrelation `\(\rho^*\)` | |-------------- |------------------------------------------------------------------------- |------------------------------------------------------------------------------ | | `\(MA(q)\)` | number of `\(ρ\)`'s sig. different from zero determines order of MA process | decreasing | | `\(AR(p)\)` | decreasing | number of `\(\rho^∗\)`'s sig. different from zero determines order of AR process | | `\(ARMA(p, q)\)` | decreasing | decreasing | --- <footer></footer> # Model Identification ### Information Criteria .smaller[ - generally, information criteria can be considered as goodness of fit measures: thus, information criteria are estimators of the _relative quality_ of statistical models for a given set of data, providing a means for model selection - information criteria estimate the relative information lost when a given model is used to represent the process generating the data (trade-off between simplicity and goodness-of-fit of the model) <br> - the smaller the estimator of an information criteria, the smaller the information loss and, thus, the better the particular model is relative to other models which are compared <br> - frequently applied information criteria are: - the Akaike information criteria (AIC), - the Bayesian information criteria (BIC), and - the Hannan-Quinn information criteria (HQIC) ] --- <footer></footer> # Model Identification ### Example .center[ <img src="data:image/png;base64,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" width="648" /> ] --- <footer></footer> # Model Identification ### Example .pull-left[ <img src="data:image/png;base64,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" 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" width="576" /> ] --- <footer></footer> # Model Identification ### Example - __test for stationarity:__ - augmented Dickey-Fuller test: `\(z(t) = -5.4346, p = 0.01\)` - __model selection:__ - choose suitable models based on (partial) autocorrelation function - reasonable candidates seem to be `\(AR(1)\)`, `\(MA(1)\)`, and `\(ARMA(1, 1)\)` --- <footer></footer> # Model Identification ### Example - __model estimation:__ .smaller[ ```r arima(series, order = c(1, 0, 0)) ``` ``` ## ## Call: ## arima(x = series, order = c(1, 0, 0)) ## ## Coefficients: ## ar1 intercept ## 0.7774 0.4637 ## s.e. 0.0360 0.2761 ## ## sigma^2 estimated as 1.16: log likelihood = -448.36, aic = 902.72 ``` ```r arima(series, order = c(0, 0, 1)) ``` ``` ## ## Call: ## arima(x = series, order = c(0, 0, 1)) ## ## Coefficients: ## ma1 intercept ## 0.7719 0.4497 ## s.e. 0.0322 0.1214 ## ## sigma^2 estimated as 1.413: log likelihood = -478.02, aic = 962.05 ``` ```r arima(series, order = c(1, 0, 1)) ``` ``` ## ## Call: ## arima(x = series, order = c(1, 0, 1)) ## ## Coefficients: ## ar1 ma1 intercept ## 0.6474 0.3556 0.4612 ## s.e. 0.0547 0.0703 0.2289 ## ## sigma^2 estimated as 1.078: log likelihood = -437.5, aic = 883 ``` ] --- <footer></footer> # Model Identification .smaller[ ```r library(forecast) ``` ``` ## Registered S3 methods overwritten by 'forecast': ## method from ## fitted.fracdiff fracdiff ## residuals.fracdiff fracdiff ``` ```r auto.arima(series, trace = TRUE) ``` ``` ## ## Fitting models using approximations to speed things up... ## ## ARIMA(2,1,2) with drift : 900.2311 ## ARIMA(0,1,0) with drift : 932.2426 ## ARIMA(1,1,0) with drift : 931.5384 ## ARIMA(0,1,1) with drift : 928.1396 ## ARIMA(0,1,0) : 930.2166 ## ARIMA(1,1,2) with drift : 888.4378 ## ARIMA(0,1,2) with drift : 913.231 ## ARIMA(1,1,1) with drift : 925.2665 ## ARIMA(1,1,3) with drift : 890.4646 ## ARIMA(0,1,3) with drift : 906.2779 ## ARIMA(2,1,1) with drift : 903.8821 ## ARIMA(2,1,3) with drift : 895.117 ## ARIMA(1,1,2) : 887.228 ## ARIMA(0,1,2) : 911.1791 ## ARIMA(1,1,1) : 923.2353 ## ARIMA(2,1,2) : 898.3981 ## ARIMA(1,1,3) : 889.2575 ## ARIMA(0,1,1) : 926.1011 ## ARIMA(0,1,3) : 904.2267 ## ARIMA(2,1,1) : 901.9089 ## ARIMA(2,1,3) : 893.3724 ## ## Now re-fitting the best model(s) without approximations... ## ## ARIMA(1,1,2) : Inf ## ARIMA(1,1,2) with drift : Inf ## ARIMA(1,1,3) : Inf ## ARIMA(1,1,3) with drift : Inf ## ARIMA(2,1,3) : Inf ## ARIMA(2,1,3) with drift : Inf ## ARIMA(2,1,2) : Inf ## ARIMA(2,1,2) with drift : Inf ## ARIMA(2,1,1) : 887.2394 ## ## Best model: ARIMA(2,1,1) ``` ``` ## Series: series ## ARIMA(2,1,1) ## ## Coefficients: ## ar1 ar2 ma1 ## 0.9667 -0.2464 -0.9894 ## s.e. 0.0567 0.0565 0.0133 ## ## sigma^2 estimated as 1.11: log likelihood=-439.55 ## AIC=887.1 AICc=887.24 BIC=901.91 ``` ] ---