Time Series Analysis

Time Series Analysis

Peforms time series analysis on assets and portfolios.

Timeseries Analysis - Screenshot

Sravz-Timeseries-Analysis-Page

Code explanation video

Timeseries Analysis

Source Code

Timeseries Notebook

Use Case

  • Verify if timeseries model can be used to predict stock price
  • Verify if the timeseries is stationary or a random work (white noise)

Analysis

  • AdjustedClose Price Vs Date
    • Price is upwards trending overtime
    • Price shows sesonality
  • AdjustedClose Price first difference vs Date
    • Plots

      pt−pt−1 p_t - p_{t-1}

      Vs Date
    • Removes trend (Upwards/Downwards movement of price)
    • Plot is centered around 0
    • Variance is still present. Lot of fluctuation around 0
    • Variance today is higher than the variance in the past (data is increasing expotentially)
  • ln(AdjustedClose Price) vs Date plot to convert exponential curve to linear curve
  • AdjustedClose Price original variance (The divergence of data from its mean value) vs Date
    • Plot 30 days moving variance with Date

      σ2=∑i=1n(xi−μ)2n \sigma^2 = \frac{\displaystyle\sum_{i=1}^{n}(x_i - \mu)^2} {n}

    • Minor variance in price does not show in the plot
  • AdjustedClose Price log variance vs Date
    • Plot 30 days log price moving variance with Date
    • Log price moving average smooths the variance
    • We see variance through out the time series
    • Minor variance in enhanced and shows in the plot
    • ln(Adjusted Close Price Variance) vs Date makes the variance relatively constant
  • ln(AdjustedClose Price) first difference vs Date
    • Enhances the variance through out the time series
    • Better represenation of variance.
    • Series is stationary (Differencing makes the timeseries stationary)
  • Auto Correlation plot - AdjustedClose Price logged first difference vs Lag Step

    rk=∑i=1N−k(Yi−Yˉ)(Yi+k−Yˉ)∑i=1N(Yi−Yˉ)2 r_{k} = \frac{\sum_{i=1}^{N-k}(Y_{i} - \bar{Y})(Y_{i+k} - \bar{Y})} {\sum_{i=1}^{N}(Y_{i} - \bar{Y})^{2} }

    • The plot for any step (upto 40) does not plot above 0.2
    • There is no signification correlation of logged price with any previous 40 lagged log price
    • There is no significant correlation (> 0.2)
      • The plot is a random walk
    • Seasonality is present if certain lags show high correlation (for Eg: Weekly, Monthly observations)
    • Trend is present if certain lags show high correlation (for Eg: Weekly, Monthly observations) and slowly decreases as the lag increases
  • Partial Auto Correlation - AdjustedClose Price logged first difference vs Lag Step that is NOT already explained by previous, lower-order lag steps
    • Refer auto correlation above
  • ARMA (autoregressive moving average) & ARIMA (autoregressive integrated moving average) will be discussed later

References