ADIDA Model

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Table of Contents

• Introduction
• ADIDA Model
• Loading libraries and data
• Explore data with the plot method
• Split the data into training and testing
• Implementation of ADIDA with StatsForecast
• Cross-validation
• Model evaluation
• References

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Introduction

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ADIDA Model

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What is intermittent demand?

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Problem with intermittent demand

1. Unpredictable variability: Intermittent demand can have unpredictable variability, making planning and forecasting difficult. Demand patterns can be irregular and fluctuate dramatically between periods with sales and periods without sales.
2. Low frequency of sales: Intermittent demand is characterized by long periods without sales. This can lead to inventory management difficulties, as it is necessary to hold enough stock to meet demand when it occurs, while avoiding excess inventory during non-sales periods.
3. Forecast error: Forecasting intermittent demand can be more difficult to pin down than constant demand. Traditional forecast models may not be adequate to capture the variability and lack of patterns in intermittent demand, which can lead to significant errors in estimates of future demand.
4. Impact on the supply chain: Intermittent demand can affect the efficiency of the supply chain and create difficulties in production planning, supplier management and logistics. Lead times and inventory levels must be adjusted to meet unpredictable demand.
5. Operating costs: Managing inventory in situations of intermittent demand can increase operating costs. Maintaining adequate inventory during non-sales periods and managing stock levels may require additional investments in storage and logistics.

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ADIDA Model

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How can you determine if the ADIDA model is suitable for a specific data set?

1. Analyze the demand pattern: Examine the demand pattern of the data to determine if it fits an intermittent pattern. Intermittent data is characterized by a high proportion of zeros and sporadic demands in specific periods.
2. Evaluate seasonality: Check if there is a clear seasonality in the data. The ADIDA model assumes that there is no seasonality or that it can be handled by temporal aggregation. If the data show complex seasonality or cannot be handled by temporal aggregation, the ADIDA model may not be suitable.
3. Data requirements: Consider the data requirements of the ADIDA model. The model requires historical demand data and the ability to calculate the mean interval between non-zero demands. Make sure you have enough data to estimate the parameters and that the data is available at a frequency suitable for temporal aggregation.
4. Performance evaluation: Perform a performance evaluation of the ADIDA model on the specific data set. Compare model-generated forecasts with actual demand values and use evaluation metrics such as mean absolute error (MAE) or mean square error (MSE). If the model performs well and produces accurate forecasts on the data set, this is an indication that it is suitable for that data set.
5. Comparison with other models: Compare the performance of the ADIDA model with other forecast models suitable for intermittent data. Consider models like Croston, Syntetos-Boylan Approximation (SBA), or models based on exponential smoothing techniques that have been developed specifically for intermittent data. If the ADIDA model shows similar or better performance than other models, it can be considered suitable.

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Loading libraries and data

Tip Statsforecast will be needed. To install, see instructions.

import matplotlib.pyplot as plt
import seaborn as sns
from statsmodels.graphics.tsaplots import plot_acf
from statsmodels.graphics.tsaplots import plot_pacf
import plotly.graph_objects as go
plt.style.use('grayscale') # fivethirtyeight  grayscale  classic
plt.rcParams['lines.linewidth'] = 1.5
dark_style = {
    'figure.facecolor': '#008080',  # #212946
    'axes.facecolor': '#008080',
    'savefig.facecolor': '#008080',
    'axes.grid': True,
    'axes.grid.which': 'both',
    'axes.spines.left': False,
    'axes.spines.right': False,
    'axes.spines.top': False,
    'axes.spines.bottom': False,
    'grid.color': '#000000',  #2A3459
    'grid.linewidth': '1',
    'text.color': '0.9',
    'axes.labelcolor': '0.9',
    'xtick.color': '0.9',
    'ytick.color': '0.9',
    'font.size': 12 }
plt.rcParams.update(dark_style)

from pylab import rcParams
rcParams['figure.figsize'] = (18,7)

import pandas as pd

df = pd.read_csv("https://raw.githubusercontent.com/Naren8520/Serie-de-tiempo-con-Machine-Learning/main/Data/tipos_malarias_choco_colombia.csv", sep=";", usecols=[0,4])
df = df.dropna()
df.head()

• The unique_id (string, int or category) represents an identifier for the series.
• The ds (datestamp) column should be of a format expected by Pandas, ideally YYYY-MM-DD for a date or YYYY-MM-DD HH:MM:SS for a timestamp.
• The y (numeric) represents the measurement we wish to forecast.

df["unique_id"]="1"
df.columns=["ds", "y", "unique_id"]
df.head()

print(df.dtypes)

ds            object
y            float64
unique_id     object
dtype: object

df["ds"] = pd.to_datetime(df["ds"])
df["y"] = df["y"].astype(float).astype("int64")

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Explore data with the plot method

from statsforecast import StatsForecast

StatsForecast.plot(df)

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Autocorrelation plots

fig, axs = plt.subplots(nrows=1, ncols=2)

plot_acf(df["y"],  lags=30, ax=axs[0],color="fuchsia")
axs[0].set_title("Autocorrelation");

plot_pacf(df["y"],  lags=30, ax=axs[1],color="lime")
axs[1].set_title('Partial Autocorrelation')

plt.show();

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Decomposition of the time series

• Level: This is the primary value that averages over time.
• Trend: The trend is the value that causes increasing or decreasing patterns in a time series.
• Seasonality: This is a cyclical event that occurs in a time series for a short time and causes short-term increasing or decreasing patterns in a time series.
• Residual/Noise: These are the random variations in the time series.

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Additive time series

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Multiplicative time series

from statsmodels.tsa.seasonal import seasonal_decompose
from plotly.subplots import make_subplots
import plotly.graph_objects as go

def plot_seasonal_decompose(
    x,
    model='additive',
    filt=None,
    period=None,
    two_sided=True,
    extrapolate_trend=0,
    title="Seasonal Decomposition"):

    result = seasonal_decompose(
            x, model=model, filt=filt, period=period,
            two_sided=two_sided, extrapolate_trend=extrapolate_trend)
    fig = make_subplots(
            rows=4, cols=1,
            subplot_titles=["Observed", "Trend", "Seasonal", "Residuals"])
    for idx, col in enumerate(['observed', 'trend', 'seasonal', 'resid']):
        fig.add_trace(
            go.Scatter(x=result.observed.index, y=getattr(result, col), mode='lines'),
                row=idx+1, col=1,
            )
    return fig

plot_seasonal_decompose(
    df["y"],
    model="additive",
    period=52,
    title="Seasonal Decomposition")

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Split the data into training and testing

train = df[df.ds<='2022-07-04'] 
test = df[df.ds>'2022-07-04']

train.shape, test.shape

((758, 3), (25, 3))

sns.lineplot(train,x="ds", y="y", label="Train", linestyle="--",linewidth=2)
sns.lineplot(test, x="ds", y="y", label="Test", linewidth=2, color="yellow")
plt.title("Falciparum Malaria");
plt.show()

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Implementation of ADIDA Model with StatsForecast

alias : str
    Custom name of the model.
prediction_intervals : Optional[ConformalIntervals]
    Information to compute conformal prediction intervals.
    By default, the model will compute the native prediction
    intervals.

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Load libraries

from statsforecast import StatsForecast
from statsforecast.models import ADIDA

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Instantiating Model

season_length = 52 # Hourly data 
horizon = len(test) # number of predictions

# We call the model that we are going to use
models = [ADIDA()]

• freq: a string indicating the frequency of the data. (See pandas’ available frequencies.)
• n_jobs: n_jobs: int, number of jobs used in the parallel processing, use -1 for all cores.
• fallback_model: a model to be used if a model fails.

sf = StatsForecast(models=models,
                   freq='7d', 
                   n_jobs=-1)

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Fit the Model

sf.fit(df=train)

StatsForecast(models=[ADIDA])

result=sf.fitted_[0,0].model_
result

{'mean': array([336.74736919])}

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Forecast Method

• h (int): represents the forecast h steps into the future. In this case, 25 week ahead.

Y_hat = sf.forecast(df=train, h=horizon)
Y_hat

sf.plot(train, Y_hat.merge(test))

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Predict method with confidence interval

• h (int): represents the forecast h steps into the future. In this case, 25 week ahead.

forecast_df = sf.predict(h=horizon) 
forecast_df.head()

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Cross-validation

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Perform time series cross-validation

• df: training data frame
• h (int): represents h steps into the future that are being forecasted. In this case, 12 months ahead.
• step_size (int): step size between each window. In other words: how often do you want to run the forecasting processes.
• n_windows(int): number of windows used for cross validation. In other words: what number of forecasting processes in the past do you want to evaluate.

crossvalidation_df = sf.cross_validation(df=df,
                                         h=horizon,
                                         step_size=30,
                                         n_windows=5)

• unique_id: series identifier
• ds: datestamp or temporal index
• cutoff: the last datestamp or temporal index for the n_windows.
• y: true value
• model: columns with the model’s name and fitted value.

crossvalidation_df

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Model Evaluation

from functools import partial

import utilsforecast.losses as ufl
from utilsforecast.evaluation import evaluate

evaluate(
    test.merge(Y_hat),
    metrics=[ufl.mae, ufl.mape, partial(ufl.mase, seasonality=season_length), ufl.rmse, ufl.smape],
    train_df=train,
)

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References

1. Changquan Huang • Alla Petukhina. Springer series (2022). Applied Time Series Analysis and Forecasting with Python.
2. Ivan Svetunkov. Forecasting and Analytics with the Augmented Dynamic Adaptive Model (ADAM)
3. James D. Hamilton. Time Series Analysis Princeton University Press, Princeton, New Jersey, 1st Edition, 1994.
4. Nixtla Parameters.
5. Pandas available frequencies.
6. Rob J. Hyndman and George Athanasopoulos (2018). “Forecasting Principles and Practice (3rd ed)”.
7. Seasonal periods- Rob J Hyndman.