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 4.38% per annum.
- UNP price at the close of May 20, 2024 was $243.63 and was higher than the top border of the primary price channel by $11.82 (5.10%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 25.12% per annum.
- UNP price at the close of May 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: March 5, 2021
End date: November 20, 2023
a = 5.5288
b = -0.0001
s = 0.0707
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0001) – 1
= -4.38%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0707) – 1
= 32.69%
March 5, 2021 calculations
Top border of price channel:
Exp(Y451)
= Exp(a + b × X451 + 2 × s)
= Exp(a + b × 654 + 2 × s)
= Exp(5.5288 + -0.0001 × 654 + 2 × 0.0707)
= Exp(5.5899)
= $267.70
Bottom border of price channel:
Exp(Y451)
= Exp(a + b × X451 – 2 × s)
= Exp(a + b × 654 – 2 × s)
= Exp(5.5288 + -0.0001 × 654 – 2 × 0.0707)
= Exp(5.3070)
= $201.74
November 20, 2023 calculations
Top border of price channel:
Exp(Y1,134)
= Exp(a + b × X1,134 + 2 × s)
= Exp(a + b × 1,644 + 2 × s)
= Exp(5.5288 + -0.0001 × 1,644 + 2 × 0.0707)
= Exp(5.4683)
= $237.05
Bottom border of price channel:
Exp(Y1,134)
= Exp(a + b × X1,134 – 2 × s)
= Exp(a + b × 1,644 – 2 × s)
= Exp(5.5288 + -0.0001 × 1,644 – 2 × 0.0707)
= Exp(5.1854)
= $178.65
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 4.38% per annum.
- UNP price at the close of May 20, 2024 was $243.63 and was higher than the top border of the primary price channel by $11.82 (5.10%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: March 8, 2023
End date: May 20, 2024
a = 4.4091
b = 0.0006
s = 0.0430
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0006) – 1
= 25.12%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0430) – 1
= 18.75%
March 8, 2023 calculations
Top border of price channel:
Exp(Y956)
= Exp(a + b × X956 + 2 × s)
= Exp(a + b × 1,387 + 2 × s)
= Exp(4.4091 + 0.0006 × 1,387 + 2 × 0.0430)
= Exp(5.3466)
= $209.89
Bottom border of price channel:
Exp(Y956)
= Exp(a + b × X956 – 2 × s)
= Exp(a + b × 1,387 – 2 × s)
= Exp(4.4091 + 0.0006 × 1,387 – 2 × 0.0430)
= Exp(5.1747)
= $176.75
May 20, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(4.4091 + 0.0006 × 1,826 + 2 × 0.0430)
= Exp(5.6161)
= $274.83
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(4.4091 + 0.0006 × 1,826 – 2 × 0.0430)
= Exp(5.4443)
= $231.43
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 25.12% per annum.
- UNP price at the close of May 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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