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 45.44% per annum.
- TMUS price at the close of January 17, 2025 was $218.97 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 64.89% per annum.
- TMUS price at the close of January 17, 2025 was higher than the top border of the secondary price channel by $0.18 (0.08%). This indicates a possible reversal in the secondary trend direction.
- 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 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: June 2, 2023
End date: January 17, 2025
a = 3.5550
b = 0.0010
s = 0.0478
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0010) – 1
= 45.44%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0478) – 1
= 21.05%
June 2, 2023 calculations
Top border of price channel:
Exp(Y848)
= Exp(a + b × X848 + 2 × s)
= Exp(a + b × 1,228 + 2 × s)
= Exp(3.5550 + 0.0010 × 1,228 + 2 × 0.0478)
= Exp(4.9108)
= $135.75
Bottom border of price channel:
Exp(Y848)
= Exp(a + b × X848 – 2 × s)
= Exp(a + b × 1,228 – 2 × s)
= Exp(3.5550 + 0.0010 × 1,228 – 2 × 0.0478)
= Exp(4.7198)
= $112.15
January 17, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(3.5550 + 0.0010 × 1,823 + 2 × 0.0478)
= Exp(5.5215)
= $250.00
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(3.5550 + 0.0010 × 1,823 – 2 × 0.0478)
= Exp(5.3305)
= $206.53
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 45.44% per annum.
- TMUS price at the close of January 17, 2025 was $218.97 and was inside the primary price channel.
Secondary Trend
Start date: November 25, 2024
End date: January 17, 2025
a = 10.5746
b = -0.0029
s = 0.0209
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0029) – 1
= -64.89%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0209) – 1
= 8.70%
November 25, 2024 calculations
Top border of price channel:
Exp(Y1,221)
= Exp(a + b × X1,221 + 2 × s)
= Exp(a + b × 1,770 + 2 × s)
= Exp(10.5746 + -0.0029 × 1,770 + 2 × 0.0209)
= Exp(5.5401)
= $254.70
Bottom border of price channel:
Exp(Y1,221)
= Exp(a + b × X1,221 – 2 × s)
= Exp(a + b × 1,770 – 2 × s)
= Exp(10.5746 + -0.0029 × 1,770 – 2 × 0.0209)
= Exp(5.4567)
= $234.31
January 17, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(10.5746 + -0.0029 × 1,823 + 2 × 0.0209)
= Exp(5.3881)
= $218.79
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(10.5746 + -0.0029 × 1,823 – 2 × 0.0209)
= Exp(5.3047)
= $201.27
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 64.89% per annum.
- TMUS price at the close of January 17, 2025 was higher than the top border of the secondary price channel by $0.18 (0.08%). 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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