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 November 20, 2024 was $233.56 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 14.59% per annum.
- UNP price at the close of November 20, 2024 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 = 5.3569
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(Y282)
= Exp(a + b × X282 + 2 × s)
= Exp(a + b × 412 + 2 × s)
= Exp(5.3569 + 0.0000 × 412 + 2 × 0.0724)
= Exp(5.4910)
= $242.50
Bottom border of price channel:
Exp(Y282)
= Exp(a + b × X282 – 2 × s)
= Exp(a + b × 412 – 2 × s)
= Exp(5.3569 + 0.0000 × 412 – 2 × 0.0724)
= Exp(5.2015)
= $181.55
November 29, 2023 calculations
Top border of price channel:
Exp(Y1,011)
= Exp(a + b × X1,011 + 2 × s)
= Exp(a + b × 1,469 + 2 × s)
= Exp(5.3569 + 0.0000 × 1,469 + 2 × 0.0724)
= Exp(5.4638)
= $235.99
Bottom border of price channel:
Exp(Y1,011)
= Exp(a + b × X1,011 – 2 × s)
= Exp(a + b × 1,469 – 2 × s)
= Exp(5.3569 + 0.0000 × 1,469 – 2 × 0.0724)
= Exp(5.1743)
= $176.67
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 0.94% per annum.
- UNP price at the close of November 20, 2024 was $233.56 and was inside the primary price channel.
Secondary Trend
Start date: September 23, 2022
End date: November 15, 2024
a = 4.8422
b = 0.0004
s = 0.0505
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0004) – 1
= 14.59%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0505) – 1
= 22.37%
September 23, 2022 calculations
Top border of price channel:
Exp(Y714)
= Exp(a + b × X714 + 2 × s)
= Exp(a + b × 1,037 + 2 × s)
= Exp(4.8422 + 0.0004 × 1,037 + 2 × 0.0505)
= Exp(5.3301)
= $206.45
Bottom border of price channel:
Exp(Y714)
= Exp(a + b × X714 – 2 × s)
= Exp(a + b × 1,037 – 2 × s)
= Exp(4.8422 + 0.0004 × 1,037 – 2 × 0.0505)
= Exp(5.1282)
= $168.71
November 15, 2024 calculations
Top border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 + 2 × s)
= Exp(a + b × 1,821 + 2 × s)
= Exp(4.8422 + 0.0004 × 1,821 + 2 × 0.0505)
= Exp(5.6226)
= $276.60
Bottom border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 – 2 × s)
= Exp(a + b × 1,821 – 2 × s)
= Exp(4.8422 + 0.0004 × 1,821 – 2 × 0.0505)
= Exp(5.4207)
= $226.04
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 14.59% per annum.
- UNP price at the close of November 20, 2024 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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