6680691 Ashita Financial Modeling and Forecasting

Holt’s Exponential Smoothing Models

The rolling price chart shows that the gap between the Upper Control Limit (UCL) and Lower Control Limit (LCL) becomes larger as the ETH price increases. For example, the gap is small during the low-price period in 2018 but much larger during the high-price periods in 2025. This means that price changes become larger when the price is higher, suggesting multiplicative behavior within the observing trend.

In order to reduce this effect, the ETH prices were log-transformed before modeling. The log transformation makes the size of the price changes more consistent over time.

Two Exponential Smoothing models were used in KNIME to compare a non-seasonal model with a seasonal model.

• Holt's Double Exponential Smoothing models: only the Level and Trend of the data and does not include seasonality.

• Holt's Triple Exponential Smoothing: models the Level, Trend, and Seasonality.

Unlike Bitcoin, Ethereum has no fixed block-reward "halving" schedule and does not follow a 4 year cycle like Bitcoin. Moreover, we could make an assumption that Ethereum's price historically moved along with Bitcoin's long-term market cycle with some sort of a correlation. Both models were applied to the price log-transformed data (Log_Price = log(Price)). The forecast results were then converted back to the original price values for evaluation.

Implemented via Java Snippet nodes were:

•      Level: Lt = α·yt + (1−α)·(Lt−1 + Tt−1)

•      Trend: Tt = β·(Lt − Lt−1) + (1−β)·Tt−1

•      Seasonality (Triple only): St = γ·(yt − Lt) + (1−γ)·St−m

•      Forecast (1-step-ahead): ŷt = Lt−1 + Tt−1 (plus St−m for Triple)

The Actual vs. Forecast plots show that both the Double and Triple Exponential Smoothing models closely follow the actual ETH prices throughout the entire period, including the major price changes in 2017, 2021, and 2025. This suggested that the Level and Trend components already explain most of the ETH price movement. Adding the seasonal component in the Triple model provides only a small improvement. Meaning that ETH's long-term price cycles are influenced mainly by the market events rather than fixed seasonal pattern.

The smoothing parameters for both models were automatically selected using KNIME's Parameter Optimization Loop. Different parameter values were tested to find the combination that produced the lowest Root Mean Squared Error (RMSE). Mean Absolute Error (MAE) and R² were also used to evaluate the model performance.

Moreover, The maximum values for α, β, and γ were limited to maximum of 0.30 because the log-transformed Ethereum data only required small smoothing values. This prevents the model from overreacting to short-term price changes and helps produce more stable forecasts.

Chosen parameters:

• Alpha (α): 0.01–0.30 (step 0.01) was chosen to test different levels of responsiveness to changes in Ethereum prices.

• Beta (β): 0.001–0.05 (step 0.001) was selected because long-term trends usually change more slowly comparing to daily price movements.

• Gamma (γ): 0.01–0.30 (step 0.01) was chosen to test different levels of seasonal smoothing while preventing the model from overreacting to temporary changes in the data.

• Small step sizes (0.01 for α and γ, and 0.001 for β) were used to allow KNIME to test many parameter combinations and identify the values that produced the lowest RMSE and the most accurate forecasts.

• The Parameter Optimization Loop automatically selected the best combination of α, β, and γ based on the lowest RMSE, ensuring the final model was optimized for the Ethereum dataset.

ARIMA

Unlike the Holt's models, which used the log-transformed price data, the ARIMA model was directly applied to the Ethereum raw data price data. Instead of using a log transformation, ARIMA used differencing (d) to make the data more stable. The dataset was split into 80% training data (2,998 rows) and 20% testing data (750 rows). KNIME's Parameter Optimization Loop was then used to automatically find the best ARIMA parameters for the model.

ARIMA Learning -> Trains the ARIMA model using the training data as it uses the historical time series data (e.g., Ethereum prices), and is based on its selected p, d, and q values.

ARIMA Predictor -> Takes the trained model from the ARIMA Learner and produces the forecast results, which can be compared with the actual prices.

Automated grid-search over (p, d, q) to minimizing RMSE, using KNIME's Parameter Optimization Loop to tested different combinations of:

• p: 0 to 5 (step = 1)

• d: 0 to 2 (step = 1)

• q: 0 to 5 (step = 1)

Each combination was used to train an ARIMA model, and the predictions were evaluated using the Root Mean Squared Error (RMSE). The model with the lowest RMSE was selected as the best ARIMA model result.

Compare Holt's Exponential Smoothing and ARIMA using an 80/20 hold-out test set.

The Numeric Scorer Node are being used to help determine the Mean Absolute Error, Root Mean Square Error, and Mean Absolute Percentage Error, which will be use to evaluate which of the model is the most appropriate for forecasting the price.

Holt's Double Exponential Smoothing -> MAE is 108.749 , RMSE is 152.443 , MAPE is 0.038%

Holt's Triple Exponential Smoothing -> MAE is 142.37 , RMSE is 234.81 , MAPE is 0.117%

ARIMA -> MAE is 904.073 , RMSE is 1017.526 , MAPE is 0.3%

As for the comparison, it seems like Holt's Double Exponential Smoothing produced the most accurate forecasts, with the lowest MAE (108.75) and RMSE (152.44). Holt's Triple Exponential Smoothing ranked second (MAE = 142.37, RMSE = 234.81), while the ARIMA model had the highest forecasting errors (MAE = 904.07, RMSE = 1,017.53). The better performance of Holt's Double model suggests that modeling only the level and trend is more suitable for Ethereum, as Ethereum doesn't need to account for seasonality compare to other cryptocurrency like Bitcoin. Therefore, Adding a fixed 1,461 day ( 4 years) seasonal component did not improve the forecasts because Ethereum does not have a strong repeating seasonal pattern comparing to the Bitcoin's halving cycle.