2.6. Temporal Analysis

2.6.1. Overview

Temporal analysis in memories-dev provides tools and methods for analyzing time-series data and temporal patterns.

2.6.2. Core Concepts

2.6.2.1. Time Series Data

Working with time series data:

from memories.temporal import TimeSeries

# Create time series
ts = TimeSeries(
    data=measurements,
    timestamps=timestamps,
    frequency="1H",
    metadata={
        "source": "sensor_network",
        "location": "san_francisco"
    }
)

# Resample time series
daily = ts.resample(
    frequency="1D",
    method="mean"
)

2.6.2.2. Temporal Decomposition

Decomposing time series:

from memories.temporal.decomposition import TimeSeriesDecomposer

# Initialize decomposer
decomposer = TimeSeriesDecomposer(
    method="stl",
    period=24,  # hours
    robust=True
)

# Perform decomposition
components = decomposer.decompose(
    time_series=ts,
    return_components=["trend", "seasonal", "residual"]
)

2.6.3. Pattern Detection

Detecting temporal patterns:

from memories.temporal.patterns import PatternDetector

# Initialize detector
detector = PatternDetector(
    methods=["fourier", "wavelets"],
    significance_level=0.05
)

# Detect patterns
patterns = detector.detect(
    time_series=ts,
    min_period=1,  # hours
    max_period=168  # hours (1 week)
)

2.6.4. Change Detection

Detecting changes in time series:

from memories.temporal.changes import ChangeDetector

# Initialize change detector
detector = ChangeDetector(
    method="cusum",
    parameters={
        "threshold": 2.0,
        "drift": 0.1
    }
)

# Detect changes
changes = detector.detect(
    time_series=ts,
    window_size="7D"
)

2.6.5. Forecasting

Time series forecasting:

from memories.temporal.forecasting import Forecaster

# Initialize forecaster
forecaster = Forecaster(
    model="prophet",
    parameters={
        "changepoint_prior_scale": 0.05,
        "seasonality_mode": "multiplicative"
    }
)

# Train model and generate forecast
forecast = await forecaster.forecast(
    time_series=ts,
    horizon="30D",
    frequency="1H",
    return_confidence_intervals=True
)

2.6.6. Temporal Correlation

Analyzing temporal correlations:

from memories.temporal.correlation import TemporalCorrelation

# Initialize correlation analyzer
correlator = TemporalCorrelation(
    methods=["pearson", "spearman", "cross_correlation"]
)

# Analyze correlations
correlations = correlator.analyze(
    time_series1=ts1,
    time_series2=ts2,
    max_lag="24H"
)

2.6.7. Visualization

Visualizing temporal data:

from memories.temporal.visualization import TimeSeriesPlotter

# Initialize plotter
plotter = TimeSeriesPlotter(
    style="seaborn",
    figure_size=(12, 6)
)

# Create time series plot
plot = plotter.plot(
    time_series=ts,
    components=["raw", "trend"],
    confidence_intervals=True
)

# Add annotations
plotter.add_events(
    events=detected_changes,
    style="vertical_lines"
)

2.6.8. Advanced Topics

Temporal Clustering - Time series clustering - Event clustering - Behavioral patterns - Temporal motifs
Anomaly Detection - Statistical methods - Machine learning - Deep learning - Ensemble methods
Causal Analysis - Granger causality - Transfer entropy - Dynamic causal modeling - Intervention analysis
Multi-scale Analysis - Wavelet analysis - Scale-space methods - Multi-resolution - Cross-scale patterns

2.6.9. Best Practices

Data Preparation - Handle missing values - Remove outliers - Normalize data - Check stationarity
Model Selection - Consider seasonality - Account for trends - Handle cyclical patterns - Validate assumptions
Performance - Optimize computations - Use efficient algorithms - Implement caching - Parallel processing
Validation - Cross-validation - Residual analysis - Model diagnostics - Performance metrics