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 5.58% per annum.
- TMUS price at the close of May 8, 2024 was $162.83 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 35.46% per annum.
- TMUS price at the close of May 8, 2024 was lower than the bottom border of the secondary price channel by $1.03 (0.63%). 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: August 7, 2020
End date: December 6, 2023
a = 4.7300
b = 0.0001
s = 0.0716
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0001) – 1
= 5.58%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0716) – 1
= 33.15%
August 7, 2020 calculations
Top border of price channel:
Exp(Y315)
= Exp(a + b × X315 + 2 × s)
= Exp(a + b × 456 + 2 × s)
= Exp(4.7300 + 0.0001 × 456 + 2 × 0.0716)
= Exp(4.9410)
= $139.91
Bottom border of price channel:
Exp(Y315)
= Exp(a + b × X315 – 2 × s)
= Exp(a + b × 456 – 2 × s)
= Exp(4.7300 + 0.0001 × 456 – 2 × 0.0716)
= Exp(4.6547)
= $105.08
December 6, 2023 calculations
Top border of price channel:
Exp(Y1,153)
= Exp(a + b × X1,153 + 2 × s)
= Exp(a + b × 1,672 + 2 × s)
= Exp(4.7300 + 0.0001 × 1,672 + 2 × 0.0716)
= Exp(5.1219)
= $167.66
Bottom border of price channel:
Exp(Y1,153)
= Exp(a + b × X1,153 – 2 × s)
= Exp(a + b × 1,672 – 2 × s)
= Exp(4.7300 + 0.0001 × 1,672 – 2 × 0.0716)
= Exp(4.8356)
= $125.91
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 5.58% per annum.
- TMUS price at the close of May 8, 2024 was $162.83 and was inside the primary price channel.
Secondary Trend
Start date: June 2, 2023
End date: April 3, 2024
a = 3.6334
b = 0.0008
s = 0.0264
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0008) – 1
= 35.46%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0264) – 1
= 11.14%
June 2, 2023 calculations
Top border of price channel:
Exp(Y1,024)
= Exp(a + b × X1,024 + 2 × s)
= Exp(a + b × 1,485 + 2 × s)
= Exp(3.6334 + 0.0008 × 1,485 + 2 × 0.0264)
= Exp(4.9210)
= $137.14
Bottom border of price channel:
Exp(Y1,024)
= Exp(a + b × X1,024 – 2 × s)
= Exp(a + b × 1,485 – 2 × s)
= Exp(3.6334 + 0.0008 × 1,485 – 2 × 0.0264)
= Exp(4.8154)
= $123.40
April 3, 2024 calculations
Top border of price channel:
Exp(Y1,233)
= Exp(a + b × X1,233 + 2 × s)
= Exp(a + b × 1,791 + 2 × s)
= Exp(3.6334 + 0.0008 × 1,791 + 2 × 0.0264)
= Exp(5.1755)
= $176.88
Bottom border of price channel:
Exp(Y1,233)
= Exp(a + b × X1,233 – 2 × s)
= Exp(a + b × 1,791 – 2 × s)
= Exp(3.6334 + 0.0008 × 1,791 – 2 × 0.0264)
= Exp(5.0699)
= $159.16
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 35.46% per annum.
- TMUS price at the close of May 8, 2024 was lower than the bottom border of the secondary price channel by $1.03 (0.63%). 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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