Avocado price forecasting with Prophet and ARIMA models

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Forecasting models for agricultural commodities

The dataset used for these analyses contains weekly retail prices of Hass avocados from various regions across the United States from 2015 to 2020. It includes columns for average price, total volume, and specific bag sizes such as small, large, and extra-large bags. Conventional avocados make up 97.2% of the market volume, while organic varieties account for only 2.8%. The average volume for conventional avocados is 1,653,212.90 units per observation period, compared to 47,811.21 for organic ones. Prices consistently show that organic avocados cost more than conventional ones, with the highest organic prices found in the Hartford/Springfield and San Francisco regions. Conversely, the cheapest conventional avocados are located in the Phoenix/Tucson area. The data reveals a clear seasonal pattern where peak monthly prices occur in September and October for both types, though conventional avocados peak specifically in October while organic ones peak in September.

Prophet, a package used for forecasting curves over time, decomposes the data into seasonality, trend-cycle, and residual components. When applied to the organic avocado data, the model was trained on the first 75% of the records and tested on the remaining 25%. The predictions for the future 365 days showed that the trend indicates an average price going down, while seasonality points to higher prices in October and lower ones from January to March. However, the results diverge significantly after the initial period immediately following the training data, seemingly missing the underlying trend. An alternative approach using ARIMA models identified "ARIMA(0,1,1)(1,1,0)[12]" as the best fit according to auto.arima. Despite this, comparisons suggest the mean model might be superior by certain metrics. Residuals indicate the model works much better for predicting prices for conventional avocados than for organic ones. The long-run forecast based on the ARIMA model expects a downward trend in prices for both types. Volatility increased each year, with the greatest volatility matching the highest prices observed in 2017.

Data processing and visualization workflows

Preparing this data required importing the CSV file into MySQL Workbench and then transferring it to a BigQuery sandbox because the data exceeded the 100 mb free limit. The process involved checking for null values, which were absent, and renaming Price Look Up columns to improve readability. SQL queries were used to calculate the average price by region and year, identify the top 10 regions with the highest average price for organic avocados, and determine which region sells the most and least avocados. The analysis also calculated the total number of bags sold by region and year and examined how volume and price changed over time. A correlation matrix revealed that total bags are highly correlated with small bags but less so with large and extra-large bags. Total volume shows a similar pattern, though the plot with small bags appears more scattered. The average price is weakly correlated with other quantities in the dataset.

Visualizations were created using Tableau Public to present findings to stakeholders. These visuals included frequency plots showing that almost no avocados are organic, which is surprising given their premium status. Time series plots confirmed that organic and conventional prices mostly mirror each other, except for one instance in late 2016 where organic prices spiked significantly relative to conventional ones. Seasonal subseries plots depict the mean of the avocado month for a specific month with blue lines and fluctuations throughout each month with black lines. The upward trend in price appears between June and September for organic avocados and June to October for conventional ones. Autocorrelation analysis showed a strong linear relationship between weeks for the first quarter, with high autocorrelation until the third lag in March. In other months, there is much less evidence for a linear relationship, leading to the conclusion that there are no consistent patterns showing a linear relationship with prices for either type. Weekly autocorrelations display a more linear relationship but with little strength. The drift method, which uses the average change of historical data as a reference, is considered the best simple method, although it ignores seasonality patterns.

Does the divergence in Prophet’s long-term predictions indicate a fundamental flaw in the model’s assumption of stable trend cycles?