Overview

Analysis Overview

Prophet Forecast Configuration

Analysis overview and configuration

Configuration

Analysis TypeProphet Decomposition
CompanyRetailCo
ObjectiveForecast daily retail sales using Prophet ML, decomposing trend and seasonality, with per-store segmented forecasts
Analysis Date2026-02-25
Processing Idtest_1772061702
Total Observations1826

Module Parameters

ParameterValue_row
forecast_periods60forecast_periods
seasonality_modeadditiveseasonality_mode
changepoint_prior_scale0.05changepoint_prior_scale
yearly_seasonalityautoyearly_seasonality
weekly_seasonalityautoweekly_seasonality
interval_width0.8interval_width
max_groups10max_groups
monthly_seasonalityFALSEmonthly_seasonality
country_holidayscountry_holidays
cross_validationFALSEcross_validation
growthlineargrowth
Prophet Decomposition analysis for RetailCo

Interpretation

Purpose

This analysis applies Facebook Prophet to forecast RetailCo's daily retail sales for the next 60 days while decomposing revenue into trend, weekly, and yearly seasonal components. Understanding these components enables the business to identify which factors drive sales variability and assess forecast reliability for planning purposes.

Key Findings

  • MAPE: 8.35% - Excellent accuracy indicates the model's predictions deviate minimally from historical actuals on average
  • Yearly Seasonality: 50.9% variance explained - The dominant driver of revenue fluctuation, showing consistent monthly/seasonal cycles
  • Weekly Seasonality: 24.7% variance explained - Strong day-of-week effects with certain days consistently 25% higher/lower than average
  • Trend: 5.5% variance explained - Weak long-term directional movement suggests relatively stable baseline revenue
  • Coverage: 79.8% - Uncertainty intervals nearly match the 80% target, validating confidence bounds for the 60-day forecast
  • Segmented Performance Variance - Category 2 achieves 16.85% MAPE while Category 6 reaches 24.98%, indicating uneven predictability across store segments

Interpretation

The model demonstrates strong predictive power driven primarily by seasonal patterns rather than trend. Yearly seasonality dominates

Data Preparation

Data Preprocessing

Data Quality & Aggregation

Data preprocessing and column mapping

Data Quality

Initial Rows10000
Final Rows1826
Rows Removed8174
Retention Rate18.3

Data Quality

MetricValue
Initial Rows10,000
Final Rows1,826
Rows Removed8,174
Retention Rate18.3%
Processed 10,000 observations, retained 1,826 (18.3%) after cleaning

Interpretation

Purpose

This section documents the data cleaning and aggregation process that transformed raw transaction data into a time series suitable for Prophet forecasting. Understanding retention rate and filtering decisions is critical because they directly impact the volume and quality of information available for the 60-day revenue forecast.

Key Findings

  • Retention Rate: 18.3% (1,826 of 10,000 rows retained) - Substantial data reduction indicates aggressive filtering or aggregation, likely consolidating daily transactions into daily revenue totals across the 1,826-day period (2013-2017)
  • Rows Removed: 8,174 observations eliminated during preprocessing - Suggests removal of duplicates, null values, or non-revenue transactions rather than random sampling
  • Final Dataset Size: 1,826 rows aligns perfectly with the analysis period (5 years of daily data) - Confirms data was aggregated to daily granularity for time series modeling

Interpretation

The 81.7% data reduction reflects intentional aggregation rather than data loss. Raw transaction-level data (10,000 rows) was consolidated into daily revenue summaries, which is appropriate for Prophet's seasonal decomposition. This preprocessing decision supports the model's ability to detect weekly and yearly patterns, as daily aggregation preserves temporal structure while reducing noise from individual transactions.

Context

Train/test split information is not

Executive Summary

Executive Summary

Key Findings & Recommendations

Key Metrics

mape
8.3516
mae
9.5657
rmse
12.1163
coverage
79.8467
forecast_periods
60
total_observations
1826
trend_strength
0.0547
weekly_strength
0.2473
n_categories
6
n_regressors
0

Key Findings

FindingValueImpact
Forecast Accuracy8.35% MAPEExcellent
Prediction Coverage79.85%Well-calibrated
Trend Contribution5.5% of varianceModerate trend
Weekly Seasonality24.7% of varianceSignificant pattern
Yearly Seasonality50.9% of varianceSignificant pattern
Category Segments6 categories modeledPer-category forecasts

Summary

Forecast Performance:
• Generated 60-day forecast with 8.35% MAPE and 79.85% coverage
Component Analysis:
• Trend explains 5.5%, weekly 24.7%, yearly 50.9% of variance
Model Configuration:
• additive seasonality mode with 25 detected changepoints
Segmented: 6 category-level forecasts generated

Interpretation

Purpose

This analysis evaluates a Prophet-based revenue forecasting model's ability to predict 60 days of future performance across six business categories. The assessment determines whether the model achieves sufficient accuracy and reliability for operational decision-making and revenue planning.

Key Findings

  • MAPE (8.35%): Excellent forecast accuracy—predictions deviate from actual values by less than 9% on average, well within acceptable thresholds for revenue forecasting
  • Coverage (79.85%): Confidence intervals capture actual outcomes 80% of the time, meeting the stated 80% target and indicating reliable uncertainty quantification
  • Yearly Seasonality (50.9%): Dominant driver of revenue variance, indicating strong seasonal cycles that the model successfully captures
  • Weekly Seasonality (24.7%): Secondary but significant pattern showing consistent day-of-week effects (±25% variance)
  • Trend Strength (5.5%): Minimal long-term directional movement, suggesting revenue stability without strong growth or decline signals

Interpretation

The model demonstrates strong predictive capability with excellent accuracy metrics and properly calibrated confidence intervals. Seasonal patterns—particularly yearly cycles—dominate revenue behavior, while trend components remain weak, indicating the business operates in a relatively stable revenue environment with predictable cyclical fluctuations. The 25 detected changepoints suggest occasional structural shifts that

Figure 4

Prophet Forecast

Historical Fit and Future Predictions

Prophet forecast with uncertainty intervals

Interpretation

Purpose

This section delivers a 60-day revenue forecast built on 5 years of historical data (2013–2017), capturing strong weekly and yearly seasonal patterns. The forecast provides point estimates with 80% confidence intervals, enabling revenue planning and risk assessment for the next two months.

Key Findings

  • MAPE of 8.35%: Excellent forecast accuracy—predictions deviate from actual values by less than 9% on average, indicating the model reliably captures revenue dynamics.
  • Coverage at 79.85%: Prediction intervals contain actual values 80% of the time (target achieved), validating the uncertainty quantification for decision-making.
  • Forecast Range: Point estimates cluster around $105–$132, with lower bounds near $73–$118 and upper bounds near $102–$149, reflecting seasonal volatility.
  • Seasonal Dominance: Weekly (24.7%) and yearly (50.9%) patterns drive 75.6% of variance, while trend contributes only 5.5%—revenue is highly cyclical, not directional.

Interpretation

The model successfully isolates revenue's repeating patterns, making it reliable for short-term planning. The tight MAPE and achieved coverage indicate Prophet's additive seasonality approach appropriately models this data. However, 18.9% unexplained residual

Figure 5

Component Decomposition

Trend and Seasonality Breakdown

Trend and seasonality components

Interpretation

Purpose

This section decomposes the revenue time series into its fundamental drivers: long-term trend, weekly cycles, and yearly seasonality. Understanding these components is essential for interpreting forecast accuracy and identifying which patterns drive revenue behavior, enabling more targeted business decisions.

Key Findings

  • Yearly Seasonality Strength: 50.9% - Dominates revenue variation, indicating strong seasonal cycles (e.g., holiday periods, fiscal quarters) that repeat annually
  • Weekly Seasonality Strength: 24.7% - Significant recurring pattern showing certain days consistently outperform or underperform others by ~25%
  • Trend Strength: 5.5% - Weak long-term growth signal; revenue is relatively stable around $120 baseline with modest 27% growth over 5 years (102.68 to 130.73)
  • Residual Variance: 18.9% - Unexplained noise suggests external factors or irregular events not captured by seasonal patterns

Interpretation

The decomposition reveals that revenue is primarily driven by predictable seasonal forces rather than sustained growth momentum. Yearly patterns (±$35) dwarf weekly fluctuations (±$25), meaning annual planning cycles matter far more than day-of-week effects. The weak trend indicates the business operates in a mature, stable market with limited organic growth—forecasts depend

Figure 6

Weekly Seasonality

Day-of-Week Revenue Patterns

Day-of-week revenue patterns

Interpretation

Purpose

This section isolates and quantifies the day-of-week revenue patterns that Prophet detected in the overall forecast model. Weekly seasonality is a critical component of the 60-day revenue forecast, explaining nearly one-quarter of the model's variance and revealing predictable cyclical behavior that repeats every seven days.

Key Findings

  • Weekly Strength: 0.247 (24.7%) - Weekly patterns account for nearly one-quarter of total revenue variance, making this the second-strongest component after yearly seasonality (50.9%)
  • Monday Effect: -20.23% - Consistently the weakest revenue day, with $24.29 below baseline
  • Sunday Peak: +17.41% - Strongest revenue day, with $20.90 above baseline
  • Weekend Surge: Saturday-Sunday combined show +30.22% uplift versus Monday-Tuesday trough of -28.27%

Interpretation

Revenue exhibits a clear weekly rhythm with a pronounced weekend peak and early-week trough. The 38-point swing between Monday's low and Sunday's high represents a substantial, repeatable pattern that the Prophet model captures with 79.8% confidence interval coverage. This cyclical behavior is reliable enough to inform 60-day forecasts and suggests consistent customer purchasing patterns tied to the calendar week.

Context

Weekly seasonality operates independently from the

Figure 7

Yearly Seasonality

Month-of-Year Revenue Patterns

Month-of-year revenue patterns

Interpretation

Purpose

This section quantifies the strength and direction of month-to-month revenue fluctuations across the year. Yearly seasonality is a critical component of the Prophet model, explaining over half of the forecast variance and enabling accurate 60-day revenue predictions by accounting for predictable calendar-driven patterns.

Key Findings

  • Yearly Strength: 0.509 (50.9%) - Dominant driver of revenue variance, second only to weekly patterns
  • Peak Revenue Months: May (+14.13%) and April (+7.41%) show strongest positive seasonal lift
  • Trough Months: January (-28.11%) and December (-25.6%) exhibit severe seasonal decline
  • Seasonal Range: 53.2 percentage-point spread between best and worst months indicates substantial predictability

Interpretation

The data reveals a pronounced bimodal seasonal pattern with spring peaks and winter troughs. January and December losses of approximately 25-28% represent the most significant seasonal headwinds, while May emerges as the strongest revenue month. This 50.9% variance contribution validates Prophet's additive seasonality approach and explains why the model achieves 8.35% MAPE—the calendar structure is highly regular and forecastable.

Context

These patterns assume consistent year-over-year behavior across the 2013-2017 analysis period. The

Table 8

Forecast Accuracy

Model Performance Metrics

Model performance metrics

MetricValue
MAPE (%)8.35
MAE ($)9.57
RMSE ($)12.12
Coverage (%)79.85
Forecast Periods60
Seasonality Modeadditive
Changepoints25

Interpretation

Purpose

This section validates the Prophet forecasting model's reliability for the 60-day revenue forecast. Accuracy metrics quantify how well the model's predictions align with historical patterns, while coverage assesses whether confidence intervals appropriately capture actual variability. Together, these metrics determine whether the forecast is trustworthy for business planning.

Key Findings

  • MAPE (8.35%): Excellent accuracy—predictions deviate from actual values by less than 10% on average, well below the "good" threshold of 10-20%
  • MAE ($9.57): Average absolute error of approximately $9.57 per forecast point, indicating consistent prediction precision
  • RMSE ($12.12): Root mean squared error slightly higher than MAE, suggesting occasional larger deviations but no systematic bias
  • Coverage (79.85%): Confidence intervals capture actual outcomes 79.85% of the time, nearly matching the 80% target, confirming proper uncertainty quantification

Interpretation

The model demonstrates strong predictive performance across all dimensions. The sub-10% MAPE reflects the model's ability to capture the strong weekly (24.7%) and yearly (50.9%) seasonality patterns identified in component analysis. Near-target coverage indicates that the 80% confidence intervals are appropriately calibrated—neither overconfident nor overly conservative. This alignment

Table 9

Changepoint Analysis

Trend Shift Dates and Magnitudes

Trend changepoint dates and magnitudes

datemagnitudeabs_magnitudedirectionrank
2014-10-05-0.16880.1688Decrease1
2014-08-08-0.1580.158Decrease2
2014-12-02-0.13890.1389Decrease3
2015-09-200.12110.1211Increase4
2014-06-10-0.12110.1211Decrease5
2015-11-170.11340.1134Increase6
2013-06-250.08490.0849Increase7
2016-01-150.07890.0789Increase8
2015-07-240.06420.0642Increase9
2013-08-220.05930.0593Increase10
2015-01-30-0.03370.0337Decrease11
2013-04-280.0050.005Increase12
2016-03-136.00e-066.00e-06Increase13
2013-10-203.00e-063.00e-06Increase14
2015-03-2900Decrease15
2016-07-0800Decrease16
2013-02-2800Increase17
2014-02-1400Decrease18
2016-05-1100Decrease19
2016-12-3000Decrease20
2013-12-1700Increase21
2014-04-1300Decrease22
2016-11-0200Decrease23
2016-09-0400Decrease24
2015-05-2600Decrease25

Interpretation

Purpose

This section identifies structural breaks in the revenue time series where the underlying trend direction shifted significantly. Detecting 25 changepoints helps explain the model's ability to capture complex revenue dynamics and validates Prophet's flexibility in handling non-linear patterns across the 5-year analysis period.

Key Findings

  • Number of Changepoints: 25 detected shifts - indicates frequent trend reversals approximately every 73 days on average
  • Changepoint Data: Table is empty - specific dates and magnitudes are not available in this summary
  • Trend Variance: Only 5.5% of total variance, suggesting changepoints are relatively modest adjustments rather than dramatic pivots

Interpretation

The 25 detected changepoints reflect a business environment with regular directional shifts in revenue patterns. Despite this complexity, the weak trend variance (5.5%) combined with strong seasonal components (75.6% combined) indicates that weekly and yearly patterns dominate revenue behavior more than underlying trend changes. This explains the model's excellent MAPE of 8.35%—seasonal patterns are more predictable than trend movements.

Context

The empty changepoint_data table limits detailed analysis of when and how severely trends shifted. The automatic detection (via 0.050 prior scale) balanced sensitivity to real changes against overfitting, supporting the model's strong validation coverage of 79.8%.

Table 10

Forecast Table

Daily Forecast Values with Bounds

Daily forecast values with confidence bounds

DatePoint_ForecastLower_BoundUpper_BoundTrendWeekly_SeasonalDay_of_Week
2018-01-0174.0559.4489.87130.7-24.29Monday
2018-01-0288.5672.15103130.8-9.659Tuesday
2018-01-0389.6274.44104.8130.8-8.429Wednesday
2018-01-0496.7980.95112.9130.8-1.054Thursday
2018-01-05104.788.47121130.87.138Friday
2018-01-06112.797.75128.5130.815.39Saturday
2018-01-07118103.3134.7130.820.9Sunday
2018-01-0872.5256.787.72130.9-24.29Monday
2018-01-0986.8970.61102.5130.9-9.659Tuesday
2018-01-1087.8771.92103130.9-8.429Wednesday
2018-01-1195.0379.24110.1130.9-1.054Thursday
2018-01-1210387.18118.1130.97.138Friday
2018-01-13111.195.81127.813115.39Saturday
2018-01-14116.6100.3131.913120.9Sunday
2018-01-1571.3355.8787.33131-24.29Monday
2018-01-1685.9670.18101.2131-9.659Tuesday
2018-01-1787.2672.45103131-8.429Wednesday
2018-01-1894.7578.55111.3131-1.054Thursday
2018-01-19103.188.66119.2131.17.138Friday
2018-01-20111.695.43126.4131.115.39Saturday
2018-01-21117.4101.9133131.120.9Sunday
2018-01-2272.557.2888.3131.1-24.29Monday
2018-01-2387.4770.75102.8131.1-9.659Tuesday
2018-01-2489.0872.41103.8131.1-8.429Wednesday
2018-01-2596.8582111.6131.2-1.054Thursday
2018-01-26105.590.3121.6131.27.138Friday
2018-01-27114.197.46130.8131.215.39Saturday
2018-01-28120.1103.9135.4131.220.9Sunday
2018-01-2975.3160.4490.82131.2-24.29Monday
2018-01-3090.3674.78105.6131.2-9.659Tuesday
2018-01-319276.38108.2131.3-8.429Wednesday
2018-02-0199.7783.59115.9131.3-1.054Thursday
2018-02-02108.393.33124.1131.37.138Friday
2018-02-03116.9101.6133.8131.315.39Saturday
2018-02-04122.8107.1137.8131.320.9Sunday
2018-02-0577.9462.694.56131.3-24.29Monday
2018-02-0692.8877.25107.6131.4-9.659Tuesday
2018-02-0794.4280.16108.6131.4-8.429Wednesday
2018-02-08102.187.5118131.4-1.054Thursday
2018-02-09110.694.47125.5131.47.138Friday
2018-02-10119.1104.1133.8131.415.39Saturday
2018-02-11125109.6140.8131.420.9Sunday
2018-02-1280.0964.6495.9131.5-24.29Monday
2018-02-1395.0679.54109.8131.5-9.659Tuesday
2018-02-1496.6681.61111.2131.5-8.429Wednesday
2018-02-15104.488.45119.6131.5-1.054Thursday
2018-02-16113.196.88129.9131.57.138Friday
2018-02-17121.8106.8138131.615.39Saturday
2018-02-18127.8111.4141.7131.620.9Sunday
2018-02-1983.1466.8798.86131.6-24.29Monday
2018-02-2098.3582.36115.5131.6-9.659Tuesday
2018-02-21100.284.15115.4131.6-8.429Wednesday
2018-02-22108.292.39123.9131.6-1.054Thursday
2018-02-23117.1102131.6131.77.138Friday
2018-02-24126.1110.3141.4131.715.39Saturday
2018-02-25132.3117.6149.3131.720.9Sunday
2018-02-2687.8872.54102.2131.7-24.29Monday
2018-02-27103.387.45119.7131.7-9.659Tuesday
2018-02-28105.389.02119.2131.7-8.429Wednesday
2018-03-01113.498.29128.8131.8-1.054Thursday

Interpretation

Purpose

This section provides the 60-day revenue forecast with confidence intervals, translating the Prophet model's learned patterns into actionable daily predictions. It serves as the primary output for understanding expected revenue trajectory and quantifying forecast uncertainty through upper and lower bounds.

Key Findings

  • Forecast Horizon: 60 days of daily predictions with 80% confidence intervals
  • Model Accuracy (MAPE): 8.35% - indicates high reliability for point estimates
  • Dominant Seasonality: Weekly patterns (24.7% variance) and yearly cycles (50.9% variance) drive daily fluctuations
  • Confidence Coverage: 79.8% - actual values fall within bounds nearly as intended, validating interval calibration

Interpretation

The forecast leverages 1,826 days of historical data to project daily revenue with strong seasonal components. Weekly patterns suggest consistent day-of-week effects (±25% variation), while yearly seasonality captures longer-term cycles. The 8.35% MAPE indicates the model's point forecasts typically deviate by less than $10 from actual values, making daily predictions reliable for planning purposes.

Context

The forecast table appears empty in the current output, but would contain date, predicted revenue, and confidence bounds. Segmented forecasts show variable accuracy across categories (16.85%–24.98%

Figure 11

Segmented Forecast

Per-Category Prophet Models

Per-category Prophet forecast with independent models per segment

Interpretation

Purpose

This section applies independent Prophet models to each of the 6 revenue categories, allowing segment-specific trend and seasonality patterns to be captured separately. This approach enables more granular forecasting than a single aggregate model, revealing whether categories behave differently and require tailored predictions for the 60-day forecast horizon.

Key Findings

  • Category Distribution: Mean category value of 3.27 with standard deviation of 1.6 indicates relatively balanced representation across segments, though slight right skew (0.51) suggests uneven category sizes
  • Forecast Range: Predicted values (yhat) average $21.88 with 80% confidence intervals spanning $15.88–$27.87, showing consistent uncertainty bands around central estimates
  • Historical Alignment: Actual values (y) average $21.93 with mean absolute deviation of ~$8.40, closely matching forecast means and validating model calibration
  • Data Completeness: 3.5% missing values in actuals occur only in forecast period (is_forecast=TRUE), as expected

Interpretation

The segmented approach reveals that individual categories maintain similar average revenue (~$21.88) but with category-specific volatility patterns. The tight alignment between historical actuals and predictions (MAPE 8.35% overall) suggests each category's independent model successfully captures its unique seasonality and trend

Table 12

Category Comparison

Forecast Accuracy by Category

Category-level forecast accuracy and revenue comparison

categoryobservationsmapeavg_daily_revenue
1182620.4119.97
2182616.8528.17
3182617.8825.07
4182618.8222.94
5182622.5416.74
687024.9815.09

Interpretation

Purpose

This section compares forecast accuracy and revenue performance across the 6 revenue categories to identify which segments are most predictable and valuable. Understanding category-level performance is critical because the overall model shows strong weekly seasonality (24.7% variance) and yearly patterns (50.9% variance) that may vary significantly by category, affecting forecast reliability for business planning.

Key Findings

  • Categories Analyzed: 6 distinct revenue segments modeled independently
  • Accuracy Range: MAPE varies from 16.85% (Category 2) to 24.98% (Category 6), indicating uneven forecast reliability across segments
  • Model Segmentation: Individual category forecasts show wider error margins than the aggregate 8.35% MAPE, suggesting category-specific volatility or data sparsity

Interpretation

The category comparison reveals that while the overall forecast achieves excellent accuracy, performance diverges significantly when disaggregated. Category 2 demonstrates strong predictability, likely driven by consistent weekly and yearly patterns, while Category 6 shows substantially higher forecast error. This variance suggests that certain revenue streams are more influenced by external factors or have weaker seasonal structure than others.

Context

The category_comparison_data table appears empty in the provided summary, limiting detailed segment analysis. The 18.3% data completeness noted in the overall analysis may disproportionately

Section 13

Model Configuration

Prophet Parameters and Settings

Prophet model parameters and settings

Prophet model with 25 detected changepoints and additive seasonality mode.

Interpretation

Purpose

This section reveals the structural complexity of the revenue time series by identifying 25 distinct trend change points over the 5-year analysis period. Understanding where and when the trend shifts is critical for accurate forecasting, as it allows Prophet to adapt its predictions to underlying business dynamics rather than assuming linear growth or decay.

Key Findings

  • Changepoints Detected: 25 automatic trend shifts - indicates substantial business volatility and multiple structural breaks in the revenue pattern
  • Changepoint Prior Scale: 0.050 - conservative setting that prevents overfitting while still capturing meaningful trend changes
  • Additive Seasonality Mode: Components combine linearly, appropriate given the strong weekly (24.7%) and yearly (50.9%) seasonal patterns that operate independently of trend level

Interpretation

The 25 changepoints suggest the business experienced significant operational, market, or strategic shifts throughout 2013-2017. These aren't random fluctuations but systematic trend reversals that Prophet learned to recognize. Combined with the additive seasonality approach, the model treats seasonal variations as fixed offsets rather than proportional to trend level—a reasonable assumption when seasonal swings remain relatively consistent regardless of overall revenue magnitude.

Context

The excellent MAPE (8.35%) and near-perfect coverage (79.8%) validate that this changepoint configuration appropriately balances flexibility with generalization. However

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