Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is decreasing.
- The decline rate of the primary trend is 0.94% per annum.
- UNP price at the close of February 20, 2025 was $247.65 and was higher than the top border of the primary price channel by $15.71 (6.77%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 12.87% per annum.
- UNP price at the close of February 20, 2025 was inside the secondary price channel.
- The direction of the secondary trend is opposite to the direction of the primary trend. This indicates a possible reversal in the direction of the primary trend.
Linear Regression Model
Model equation:
Yi = α + β × Xi + εi
Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)
Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)
where:
i - observation number
Yi - natural logarithm of UNP price
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e
Primary Trend
Start date: January 6, 2021
End date: November 29, 2023
a = 5.3488
b = 0.0000
s = 0.0724
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0000) – 1
= -0.94%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0724) – 1
= 33.57%
January 6, 2021 calculations
Top border of price channel:
Exp(Y221)
= Exp(a + b × X221 + 2 × s)
= Exp(a + b × 320 + 2 × s)
= Exp(5.3488 + 0.0000 × 320 + 2 × 0.0724)
= Exp(5.4853)
= $241.12
Bottom border of price channel:
Exp(Y221)
= Exp(a + b × X221 – 2 × s)
= Exp(a + b × 320 – 2 × s)
= Exp(5.3488 + 0.0000 × 320 – 2 × 0.0724)
= Exp(5.1958)
= $180.52
November 29, 2023 calculations
Top border of price channel:
Exp(Y950)
= Exp(a + b × X950 + 2 × s)
= Exp(a + b × 1,377 + 2 × s)
= Exp(5.3488 + 0.0000 × 1,377 + 2 × 0.0724)
= Exp(5.4580)
= $234.64
Bottom border of price channel:
Exp(Y950)
= Exp(a + b × X950 – 2 × s)
= Exp(a + b × 1,377 – 2 × s)
= Exp(5.3488 + 0.0000 × 1,377 – 2 × 0.0724)
= Exp(5.1686)
= $175.66
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 0.94% per annum.
- UNP price at the close of February 20, 2025 was $247.65 and was higher than the top border of the primary price channel by $15.71 (6.77%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: September 22, 2022
End date: February 20, 2025
a = 4.9214
b = 0.0003
s = 0.0516
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0003) – 1
= 12.87%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0516) – 1
= 22.92%
September 22, 2022 calculations
Top border of price channel:
Exp(Y652)
= Exp(a + b × X652 + 2 × s)
= Exp(a + b × 944 + 2 × s)
= Exp(4.9214 + 0.0003 × 944 + 2 × 0.0516)
= Exp(5.3378)
= $208.05
Bottom border of price channel:
Exp(Y652)
= Exp(a + b × X652 – 2 × s)
= Exp(a + b × 944 – 2 × s)
= Exp(4.9214 + 0.0003 × 944 – 2 × 0.0516)
= Exp(5.1314)
= $169.26
February 20, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(4.9214 + 0.0003 × 1,826 + 2 × 0.0516)
= Exp(5.6304)
= $278.78
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(4.9214 + 0.0003 × 1,826 – 2 × 0.0516)
= Exp(5.4241)
= $226.80
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 12.87% per annum.
- UNP price at the close of February 20, 2025 was inside the secondary price channel.
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
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