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 4.42% per annum.
- UNP price at the close of April 26, 2024 was $242.79 and was higher than the top border of the primary price channel by $10.42 (4.49%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 28.40% per annum.
- UNP price at the close of April 26, 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: March 8, 2021
End date: November 20, 2023
a = 5.5327
b = -0.0001
s = 0.0707
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0001) – 1
= -4.42%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0707) – 1
= 32.66%
March 8, 2021 calculations
Top border of price channel:
Exp(Y468)
= Exp(a + b × X468 + 2 × s)
= Exp(a + b × 679 + 2 × s)
= Exp(5.5327 + -0.0001 × 679 + 2 × 0.0707)
= Exp(5.5900)
= $267.73
Bottom border of price channel:
Exp(Y468)
= Exp(a + b × X468 – 2 × s)
= Exp(a + b × 679 – 2 × s)
= Exp(5.5327 + -0.0001 × 679 – 2 × 0.0707)
= Exp(5.3073)
= $201.81
November 20, 2023 calculations
Top border of price channel:
Exp(Y1,150)
= Exp(a + b × X1,150 + 2 × s)
= Exp(a + b × 1,666 + 2 × s)
= Exp(5.5327 + -0.0001 × 1,666 + 2 × 0.0707)
= Exp(5.4679)
= $236.95
Bottom border of price channel:
Exp(Y1,150)
= Exp(a + b × X1,150 – 2 × s)
= Exp(a + b × 1,666 – 2 × s)
= Exp(5.5327 + -0.0001 × 1,666 – 2 × 0.0707)
= Exp(5.1852)
= $178.62
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 4.42% per annum.
- UNP price at the close of April 26, 2024 was $242.79 and was higher than the top border of the primary price channel by $10.42 (4.49%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: March 9, 2023
End date: April 10, 2024
a = 4.2855
b = 0.0007
s = 0.0418
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0007) – 1
= 28.40%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0418) – 1
= 18.18%
March 9, 2023 calculations
Top border of price channel:
Exp(Y973)
= Exp(a + b × X973 + 2 × s)
= Exp(a + b × 1,410 + 2 × s)
= Exp(4.2855 + 0.0007 × 1,410 + 2 × 0.0418)
= Exp(5.3347)
= $207.41
Bottom border of price channel:
Exp(Y973)
= Exp(a + b × X973 – 2 × s)
= Exp(a + b × 1,410 – 2 × s)
= Exp(4.2855 + 0.0007 × 1,410 – 2 × 0.0418)
= Exp(5.1676)
= $175.50
April 10, 2024 calculations
Top border of price channel:
Exp(Y1,246)
= Exp(a + b × X1,246 + 2 × s)
= Exp(a + b × 1,808 + 2 × s)
= Exp(4.2855 + 0.0007 × 1,808 + 2 × 0.0418)
= Exp(5.6073)
= $272.40
Bottom border of price channel:
Exp(Y1,246)
= Exp(a + b × X1,246 – 2 × s)
= Exp(a + b × 1,808 – 2 × s)
= Exp(4.2855 + 0.0007 × 1,808 – 2 × 0.0418)
= Exp(5.4402)
= $230.49
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 28.40% per annum.
- UNP price at the close of April 26, 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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