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 6.55% per annum.
- TMO price at the close of March 28, 2025 was $500.16 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 1.03% per annum.
- TMO price at the close of March 28, 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 TMO 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: July 29, 2021
End date: January 5, 2024
a = 6.4759
b = -0.0002
s = 0.0593
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0002) – 1
= -6.55%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0593) – 1
= 26.79%
July 29, 2021 calculations
Top border of price channel:
Exp(Y336)
= Exp(a + b × X336 + 2 × s)
= Exp(a + b × 486 + 2 × s)
= Exp(6.4759 + -0.0002 × 486 + 2 × 0.0593)
= Exp(6.5045)
= $668.13
Bottom border of price channel:
Exp(Y336)
= Exp(a + b × X336 – 2 × s)
= Exp(a + b × 486 – 2 × s)
= Exp(6.4759 + -0.0002 × 486 – 2 × 0.0593)
= Exp(6.2671)
= $526.95
January 5, 2024 calculations
Top border of price channel:
Exp(Y949)
= Exp(a + b × X949 + 2 × s)
= Exp(a + b × 1,376 + 2 × s)
= Exp(6.4759 + -0.0002 × 1,376 + 2 × 0.0593)
= Exp(6.3394)
= $566.46
Bottom border of price channel:
Exp(Y949)
= Exp(a + b × X949 – 2 × s)
= Exp(a + b × 1,376 – 2 × s)
= Exp(6.4759 + -0.0002 × 1,376 – 2 × 0.0593)
= Exp(6.1020)
= $446.75
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 6.55% per annum.
- TMO price at the close of March 28, 2025 was $500.16 and was inside the primary price channel.
Secondary Trend
Start date: February 11, 2022
End date: March 10, 2025
a = 6.2670
b = 0.0000
s = 0.0647
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0000) – 1
= 1.03%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0647) – 1
= 29.55%
February 11, 2022 calculations
Top border of price channel:
Exp(Y473)
= Exp(a + b × X473 + 2 × s)
= Exp(a + b × 683 + 2 × s)
= Exp(6.2670 + 0.0000 × 683 + 2 × 0.0647)
= Exp(6.4156)
= $611.28
Bottom border of price channel:
Exp(Y473)
= Exp(a + b × X473 – 2 × s)
= Exp(a + b × 683 – 2 × s)
= Exp(6.2670 + 0.0000 × 683 – 2 × 0.0647)
= Exp(6.1567)
= $471.86
March 10, 2025 calculations
Top border of price channel:
Exp(Y1,242)
= Exp(a + b × X1,242 + 2 × s)
= Exp(a + b × 1,806 + 2 × s)
= Exp(6.2670 + 0.0000 × 1,806 + 2 × 0.0647)
= Exp(6.4471)
= $630.85
Bottom border of price channel:
Exp(Y1,242)
= Exp(a + b × X1,242 – 2 × s)
= Exp(a + b × 1,806 – 2 × s)
= Exp(6.2670 + 0.0000 × 1,806 – 2 × 0.0647)
= Exp(6.1882)
= $486.96
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 1.03% per annum.
- TMO price at the close of March 28, 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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