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H7 Time Series Analysis

Time whatttt?

  • Analyse van data die geordend is in tijd over een bepaalde periode
    • bv Supermarkt: hoeveelheid verkochte producten per dag
    • bv Aandelen: prijs van een aandeel per dag
  • Op deze data kunnen we dan voorspellingen maken
    • bv Supermarkt: hoeveelheid verkochte producten per dag in de toekomst
    • bv Aandelen: prijs van een aandeel per dag in de toekomst

Components of Time Series

  • Trend: de algemene richting van de data
    • bv stijgend, dalend, constant
  • Seasonality: herhaling van patronen in de data
    • bv. elke maandag is er een piek in de verkoop
  • Noise: onregelmatigheden in de data
    • random variaties die niet te verklaren zijn door de trend of seasonality
  • Cyclical: herhaling van patronen in de data die niet op een vaste tijdsinterval gebeuren

moving averages

simple moving average

```py
# simple moving average
data['SMA3'] = data['Close'].rolling(window=3).mean()
data['SMA5'] = data['Close'].rolling(window=5).mean()
data['SMA10'] = data['Close'].rolling(window=10).mean()

# Simple moving average with shift -> to predict the future je zet ze een rij naar onder op de plek waar dit de predictie is voor die dag bv
data['SMA3_forecast'] = data['Close'].rolling(3).mean().shift(1)
data['SMA5_forecast'] = data['Close'].rolling(5).mean().shift(1)
data['SMA10_forecast'] = data['Close'].rolling(10).mean().shift(1)
```

weighted moving average -> recentere data krijgt meer gewicht

  • exponential moving average If $\alpha$ is close to 0, then 1 − $\alpha$ is close to 1 and the weights decrease very slowly. In other words, observations from the distant past continue to have a large influence on the next forecast. This means that the graph of the forecasts will be relatively smooth, just as with a large span in the moving averages method. But if $\alpha$ is close to 1, the weights decrease rapidly, and only very recent observations have much influence on the next forecast.

    # exponential moving average
# alpha
data['EMA_0.1'] = data['Close'].ewm(alpha=.1, adjust=False).mean()
data['EMA_0.5'] = data['Close'].ewm(alpha=.5, adjust=False).mean()

Exponential smoothing

single exponential smoothing

-> exponential moving average (EMA)

-> geen trend of seasonality

# single exponential smoothing
# smoothing_level=0.1 -> alpha
from statsmodels.tsa.holtwinters import SimpleExpSmoothing
data_ses = SimpleExpSmoothing(data['Close']).fit(smoothing_level=0.1, optimized=True)
data['SES'] = data_ses.fittedvalues
data.head()

data.plot(y=['Close',  'SES'], figsize=[10,5])

#Predicting the future
data_ses_fcast = data_ses.forecast(12)

data.plot(y=['Close',  'SES'], figsize=[10,5])
data_ses_fcast.plot(marker='.', legend=True, label='Forecast')

double exponential smoothing

-> Holt's method

-> trend maar geen seasonality

# double exponential smoothing
from statsmodels.tsa.api import Holt

data_des = Holt(data['Close']).fit(smoothing_level=.1, smoothing_trend=.2)

data['DES'] = data_des.fittedvalues

data.plot(y=['Close',  'DES'], figsize=[10,5])

#Predicting the future
data_des_fcast = data_des.forecast(12)

data['number_of_heavily_wounded'].plot(marker='o', legend=True) # Observations
data['DES'].plot(legend=True, label='DES fitted values', figsize=[10,5])
data_ses_fcast.plot(marker='.', legend=True, label='Forecast SES')
data_des_fcast.plot(marker='.', legend=True, label='Forecast DES')

triple exponential smoothing

-> Holt-Winters method

-> trend en seasonality

2 Soorten:

  • additive
    • seasonality is constant add
  • multiplicative
    • seasonality is not constant mul
# triple exponential smoothing
# je kunt de freq aanpassen naar bv D voor days of MS voor months
# additive
from statsmodels.tsa.holtwinters import ExponentialSmoothing

train = data.number_of_heavily_wounded
test = data.number_of_heavily_wounded

model = ExponentialSmoothing(train,
  trend='add', seasonal='add',
  seasonal_periods=12, freq='MS').fit()

train.plot(legend=True, label='train')
test.plot(legend=True, label='test')
model.fittedvalues.plot(legend=True, label='fitted')

# multiplicative
from statsmodels.tsa.holtwinters import ExponentialSmoothing

train = data.number_of_heavily_wounded
test = data.number_of_heavily_wounded

model = ExponentialSmoothing(train,
  trend='add', seasonal='mul',
  seasonal_periods=12, freq='MS').fit()

train.plot(legend=True, label='train')
test.plot(legend=True, label='test')
model.fittedvalues.plot(legend=True, label='fitted')

#Predicting the future
model_predicted = model.forecast(12)

train.plot(legend=True, label='train')
model.fittedvalues.plot(legend=True, label='fitted')

test.plot(legend=True, label='test')
model_predicted.plot(legend=True, label='predicted')

plt.title('Train, test, fitted & predicted values using Holt-Winters')

Model ìnternals

# Model internals: last estimate for level, trend and seasonal factors:
print(f'level: {wounded_hw.level[83]}')
print(f'trend: {wounded_hw.trend[83]}')
print(f'seasonal factor: {wounded_hw.season[72:84]}')