Introd u ction to the Co u rse TIME SE R IE S AN ALYSIS IN P YTH ON Rob Reider Adj u nct Professor , NYU - Co u rant Cons u ltant , Q u antopian
E x ample of Time Series : Google Trends TIME SERIES ANALYSIS IN PYTHON
E x ample of Time Series : Climate Data TIME SERIES ANALYSIS IN PYTHON
E x ample of Time Series : Q u arterl y Earnings Data TIME SERIES ANALYSIS IN PYTHON
E x ample of M u ltiple Series : Nat u ral Gas and Heating Oil TIME SERIES ANALYSIS IN PYTHON
Goals of Co u rse Learn abo u t time series models Fit data to a times series model Use the models to make forecasts of the f u t u re Learn ho w to u se the rele v ant statistical packages in P y thon Pro v ide concrete e x amples of ho w these models are u sed TIME SERIES ANALYSIS IN PYTHON
Some Usef u l Pandas Tools Changing an inde x to datetime df.index = pd.to_datetime(df.index) Plo � ing data df.plot() Slicing data df['2012'] TIME SERIES ANALYSIS IN PYTHON
Some Usef u l Pandas Tools Join t w o DataFrames df1.join(df2) Resample data ( e . g . from dail y to w eekl y) df = df.resample(rule='W', how='last') TIME SERIES ANALYSIS IN PYTHON
More pandas F u nctions Comp u ting percent changes and di � erences of a time series df['col'].pct_change() df['col'].diff() pandas correlation method of Series df['ABC'].corr(df['XYZ']) pandas a u tocorrelation df['ABC'].autocorr() TIME SERIES ANALYSIS IN PYTHON
Let ' s practice ! TIME SE R IE S AN ALYSIS IN P YTH ON
Correlation of T w o Time Series TIME SE R IE S AN ALYSIS IN P YTH ON Rob Reider Adj u nct Professor , NYU - Co u rant Cons u ltant , Q u antopian
Correlation of T w o Time Series Plot of S & P 500 and JPMorgan stock TIME SERIES ANALYSIS IN PYTHON
Correlation of T w o Time Series Sca � er plot of S & P 500 and JP Morgan ret u rns TIME SERIES ANALYSIS IN PYTHON
More Scatter Plots Correlation = 0.9 Correlation = 0.4 Correlation = -0.9 Corelation = 1.0 TIME SERIES ANALYSIS IN PYTHON
Common Mistake : Correlation of T w o Trending Series Do w Jones Ind u strial A v erage and UFO Sightings ( www. n u forc . org ) Correlation of le v els : 0.94 Correlation of percent changes : ≈ 0 TIME SERIES ANALYSIS IN PYTHON
E x ample : Correlation of Large Cap and Small Cap Stocks Start w ith stock prices of SPX ( large cap ) and R 2000 ( small cap ) First step : Comp u te percentage changes of both series df['SPX_Ret'] = df['SPX_Prices'].pct_change() df['R2000_Ret'] = df['R2000_Prices'].pct_change() TIME SERIES ANALYSIS IN PYTHON
E x ample : Correlation of Large Cap and Small Cap Stocks Vis u ali z e correlation w ith sca � ter plot plt.scatter(df['SPX_Ret'], df['R2000_Ret']) plt.show() TIME SERIES ANALYSIS IN PYTHON
E x ample : Correlation of Large Cap and Small Cap Stocks Use pandas correlation method for Series correlation = df['SPX_Ret'].corr(df['R2000_Ret']) print("Correlation is: ", correlation) Correlation is: 0.868 TIME SERIES ANALYSIS IN PYTHON
Let ' s practice ! TIME SE R IE S AN ALYSIS IN P YTH ON
Simple Linear Regressions TIME SE R IE S AN ALYSIS IN P YTH ON Rob Reider Adj u nct Professor , NYU - Co u rant Cons u ltant , Q u antopian
What is a Regression ? Simple linear regression : y = α + βx + ϵ t t t TIME SERIES ANALYSIS IN PYTHON
What is a Regression ? Ordinar y Least Sq u ares ( OLS ) TIME SERIES ANALYSIS IN PYTHON
P y thon Packages to Perform Regressions Warning : the order of x and In statsmodels : y is not consistent across import statsmodels.api as sm sm.OLS(y, x).fit() packages In n u mp y: np.polyfit(x, y, deg=1) In pandas : pd.ols(y, x) In scip y: from scipy import stats stats.linregress(x, y) TIME SERIES ANALYSIS IN PYTHON
E x ample : Regression of Small Cap Ret u rns on Large Cap Import the statsmodels mod u le import statsmodels.api as sm As before , comp u te percentage changes in both series df['SPX_Ret'] = df['SPX_Prices'].pct_change() df['R2000_Ret'] = df['R2000_Prices'].pct_change() Add a constant to the DataFrame for the regression intercept df = sm.add_constant(df) TIME SERIES ANALYSIS IN PYTHON
Regression E x ample ( contin u ed ) Notice that the � rst ro w of ret u rns is NaN SPX_Price R2000_Price SPX_Ret R2000_Ret Date 2012-11-01 1427.589966 827.849976 NaN NaN 2012-11-02 1414.199951 814.369995 -0.009379 -0.016283 Delete the ro w of NaN df = df.dropna() R u n the regression results = sm.OLS(df['R2000_Ret'],df[['const','SPX_Ret']]).fit() print(results.summary()) TIME SERIES ANALYSIS IN PYTHON
Regression E x ample ( contin u ed ) Regression o u tp u t Intercept in results.params[0] Slope in results.params[1] TIME SERIES ANALYSIS IN PYTHON
Regression E x ample ( contin u ed ) Regression o u tp u t TIME SERIES ANALYSIS IN PYTHON
Relationship Bet w een R - Sq u ared and Correlation 2 2 [corr( x , y )] = R ( or R - sq u ared ) sign(corr) = sign(regression slope) In last e x ample : R - Sq u ared = 0.753 Slope is positi v e √0.753 correlation = + = 0.868 TIME SERIES ANALYSIS IN PYTHON
Let ' s practice ! TIME SE R IE S AN ALYSIS IN P YTH ON
A u tocorrelation TIME SE R IE S AN ALYSIS IN P YTH ON Rob Reider Adj u nct Professor , NYU - Co u rant Cons u ltant , Q u antopian
What is A u tocorrelation ? Correlation of a time series w ith a lagged cop y of itself Lag - one a u tocorrelation Also called serial correlation TIME SERIES ANALYSIS IN PYTHON
Interpretation of A u tocorrelation Mean Re v ersion - Negati v e a u tocorrelation TIME SERIES ANALYSIS IN PYTHON
Interpretation of A u tocorrelation Moment u m , or Trend Follo w ing - Positi v e a u tocorrelation TIME SERIES ANALYSIS IN PYTHON
Traders Use A u tocorrelation to Make Mone y Indi v id u al stocks Historicall y ha v e negati v e a u tocorrelation Meas u red o v er short hori z ons ( da y s ) Trading strateg y: B uy losers and sell w inners Commodities and c u rrencies Historicall y ha v e positi v e a u tocorrelation Meas u red o v er longer hori z ons ( months ) Trading strateg y: B uy w inners and sell losers TIME SERIES ANALYSIS IN PYTHON
E x ample of Positi v e A u tocorrelation : E x change Rates Use dail y ¥ /$ e x change rates in DataFrame df from FRED Con v ert inde x to datetime # Convert index to datetime df.index = pd.to_datetime(df.index) # Downsample from daily to monthly data df = df.resample(rule='M', how='last') # Compute returns from prices df['Return'] = df['Price'].pct_change() # Compute autocorrelation autocorrelation = df['Return'].autocorr() print("The autocorrelation is: ",autocorrelation) The autocorrelation is: 0.0567 TIME SERIES ANALYSIS IN PYTHON
Let ' s practice ! TIME SE R IE S AN ALYSIS IN P YTH ON
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