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 5.93% per annum.
- TMO price at the close of May 7, 2024 was $572.87 and was higher than the top border of the primary price channel by $6.43 (1.14%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 87.28% per annum.
- TMO price at the close of May 7, 2024 was lower than the bottom border of the secondary price channel by $33.41 (5.51%). 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 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 30, 2021
End date: February 21, 2024
a = 6.5244
b = -0.0002
s = 0.0604
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0002) – 1
= -5.93%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0604) – 1
= 27.31%
July 30, 2021 calculations
Top border of price channel:
Exp(Y562)
= Exp(a + b × X562 + 2 × s)
= Exp(a + b × 814 + 2 × s)
= Exp(6.5244 + -0.0002 × 814 + 2 × 0.0604)
= Exp(6.5088)
= $671.04
Bottom border of price channel:
Exp(Y562)
= Exp(a + b × X562 – 2 × s)
= Exp(a + b × 814 – 2 × s)
= Exp(6.5244 + -0.0002 × 814 – 2 × 0.0604)
= Exp(6.2674)
= $527.08
February 21, 2024 calculations
Top border of price channel:
Exp(Y1,205)
= Exp(a + b × X1,205 + 2 × s)
= Exp(a + b × 1,750 + 2 × s)
= Exp(6.5244 + -0.0002 × 1,750 + 2 × 0.0604)
= Exp(6.3521)
= $573.70
Bottom border of price channel:
Exp(Y1,205)
= Exp(a + b × X1,205 – 2 × s)
= Exp(a + b × 1,750 – 2 × s)
= Exp(6.5244 + -0.0002 × 1,750 – 2 × 0.0604)
= Exp(6.1106)
= $450.62
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 5.93% per annum.
- TMO price at the close of May 7, 2024 was $572.87 and was higher than the top border of the primary price channel by $6.43 (1.14%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: October 12, 2023
End date: March 28, 2024
a = 3.3304
b = 0.0017
s = 0.0310
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0017) – 1
= 87.28%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0310) – 1
= 13.18%
October 12, 2023 calculations
Top border of price channel:
Exp(Y1,116)
= Exp(a + b × X1,116 + 2 × s)
= Exp(a + b × 1,618 + 2 × s)
= Exp(3.3304 + 0.0017 × 1,618 + 2 × 0.0310)
= Exp(6.1736)
= $479.93
Bottom border of price channel:
Exp(Y1,116)
= Exp(a + b × X1,116 – 2 × s)
= Exp(a + b × 1,618 – 2 × s)
= Exp(3.3304 + 0.0017 × 1,618 – 2 × 0.0310)
= Exp(6.0498)
= $424.02
March 28, 2024 calculations
Top border of price channel:
Exp(Y1,231)
= Exp(a + b × X1,231 + 2 × s)
= Exp(a + b × 1,786 + 2 × s)
= Exp(3.3304 + 0.0017 × 1,786 + 2 × 0.0310)
= Exp(6.4624)
= $640.61
Bottom border of price channel:
Exp(Y1,231)
= Exp(a + b × X1,231 – 2 × s)
= Exp(a + b × 1,786 – 2 × s)
= Exp(3.3304 + 0.0017 × 1,786 – 2 × 0.0310)
= Exp(6.3386)
= $565.99
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 87.28% per annum.
- TMO price at the close of May 7, 2024 was lower than the bottom border of the secondary price channel by $33.41 (5.51%). 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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