Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is increasing.
- The growth rate of the primary trend is 89.79% per annum.
- TMUS price at the close of November 19, 2024 was $233.20 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 205.94% per annum.
- TMUS price at the close of November 19, 2024 was lower than the bottom border of the secondary price channel by $0.77 (0.33%). This indicates a possible reversal in the secondary trend direction.
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 TMUS 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: April 5, 2024
End date: November 19, 2024
a = 2.2304
b = 0.0018
s = 0.0256
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0018) – 1
= 89.79%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0256) – 1
= 10.77%
April 5, 2024 calculations
Top border of price channel:
Exp(Y1,099)
= Exp(a + b × X1,099 + 2 × s)
= Exp(a + b × 1,598 + 2 × s)
= Exp(2.2304 + 0.0018 × 1,598 + 2 × 0.0256)
= Exp(5.0868)
= $161.87
Bottom border of price channel:
Exp(Y1,099)
= Exp(a + b × X1,099 – 2 × s)
= Exp(a + b × 1,598 – 2 × s)
= Exp(2.2304 + 0.0018 × 1,598 – 2 × 0.0256)
= Exp(4.9845)
= $146.13
November 19, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(2.2304 + 0.0018 × 1,826 + 2 × 0.0256)
= Exp(5.4870)
= $241.54
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(2.2304 + 0.0018 × 1,826 – 2 × 0.0256)
= Exp(5.3847)
= $218.05
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 89.79% per annum.
- TMUS price at the close of November 19, 2024 was $233.20 and was inside the primary price channel.
Secondary Trend
Start date: September 18, 2024
End date: November 19, 2024
a = -0.1106
b = 0.0031
s = 0.0142
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0031) – 1
= 205.94%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0142) – 1
= 5.83%
September 18, 2024 calculations
Top border of price channel:
Exp(Y1,213)
= Exp(a + b × X1,213 + 2 × s)
= Exp(a + b × 1,764 + 2 × s)
= Exp(-0.1106 + 0.0031 × 1,764 + 2 × 0.0142)
= Exp(5.3219)
= $204.78
Bottom border of price channel:
Exp(Y1,213)
= Exp(a + b × X1,213 – 2 × s)
= Exp(a + b × 1,764 – 2 × s)
= Exp(-0.1106 + 0.0031 × 1,764 – 2 × 0.0142)
= Exp(5.2652)
= $193.49
November 19, 2024 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(-0.1106 + 0.0031 × 1,826 + 2 × 0.0142)
= Exp(5.5119)
= $247.61
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(-0.1106 + 0.0031 × 1,826 – 2 × 0.0142)
= Exp(5.4552)
= $233.97
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 205.94% per annum.
- TMUS price at the close of November 19, 2024 was lower than the bottom border of the secondary price channel by $0.77 (0.33%). This indicates a possible reversal in the secondary trend direction.
- 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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